The Standard Normal Distribution

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Questions

• How can I calculate standard normal probabilities on the TI-84?
• Use the standard normal distribution to find #P(z lt 1.96)#.
• What are the median and the mode of the standard normal distribution?
• What is the variance of the standard normal distribution?
• What is the area under the standard normal distribution between z = -1.69 and z = 1.00
• What is z value corresponding to the 65th percentile of the standard normal distribution?
• What is the z value such that 52% of the data are to its left?
• What are the 2 z values that identify the middle 50% of the standard normal distribution?
• How do I use the empirical rule?
• Use the empirical rule to determine the approximate probability that a z value is between -1 and 1 on the standard normal curve.
• Use the empirical rule to determine the approximate probability that a z value is between 0 and 1 on the standard normal curve.
• Use the empirical rule to determine the approximate probability that a z value is between -2 and 0 on the standard normal curve.
• What does the Empirical Rule (also called the 68-95-99.7 Rule) tell you about the approximate probabilities for normally distributed values?
• Question #e0a65
• What defines a normal distribution?
• How does the normal distribution differ form the Poisson distribution?
• What is the mathematical difference between the probability density functions of a normal distribution and a standard normal distribution?
• What is the mathematical formula for the probability density function of the general normal distribution?
• Do all random distributions follow a "normal" distribution?
• What is the standard deviation of the standard normal distribution?
• What is the Gaussian function?
• What determines if data will follow a normal distribution?
• What is the skewness of a normal distribution?
• What is the difference between a normal distribution, binomial distribution, and a Poisson distribution?
• What is the Gaussian function?
• Is the sum of two Gaussian functions still a Gaussian function? What implication does this have for adding data sets?
• Question #cef5e
• Which probability distributions are considered "bell-shaped?"
• Why does the standard normal distribution have a kurtosis of 0?
• What is the characteristic function of a normal distribution?
• What is the moment generating function of a Gaussian distribution?
• Suppose that the fish in my pond have mean length 20 inches with a standard deviation of 4 inches. What is the probability that in an independent random sample, the total length of 5 fish caught from this pond will be between 95 and 110 inches in length?
• Question #813cd
• Question #54e89
• How do you determine the percentage of eruptions that last between 92 and 116 seconds with a mean of 104 and a standard deviation of 6?
• A placement exam for entrance into a math class yields a mean of 80 and a standard deviation of 10. How do you find the percentage of scores that lie between 60 and 80?
• Assume that a normal distribution has a mean of 21 and a standard deviation of 2. What is the percentage of values that lie above 23?
• Why is the empirical rule important?
• The mean value of a land and building per acre from a sample of a farm is $1500, with a standard deviation of $200. What is the percent of farms whose land and building values acre are between $1300 and $1700?
• The heights of women at a large university are approximately bell-shaped, with a mean of 64 inches and standard deviation of 2 inches. What is the probability that a randomly selected woman from this university is 66 inches or taller?
• For a normal distribution, what is the percentage of data that is between #mu - 0.5 sigma# and #mu + 0.5 sigma#?
• There is a normal distribution with min = 4, max = 16 and mean = 10. What is the standard deviation?
• How can I tell if my data is normally distributed? Do the mean, median and mode have to be identical for it to be a normal distribution?
• How does central tendency relate to normal distribution?
• How can you use normal distribution to approximate the binomial distribution?
• What is the 90th percentile of a standard normal distribution?
• Using a standard normal distribution, what is #P(z < -1.96 or z > 1.96)#?
• How do I find the area under the normal distribution curve given the z-score or interval?
• IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability of a score greater than 110?
• For the standard normal distribution, what percentage of values are smaller than z = -1.50?
• For the standard normal distribution, what percentage of values are greater than z = 0.67?
• For a normal distribution, what is the probability that the data falls somewhere .5 standard deviations from the mean?
• Let's say that the spread of possible outcomes is 1 to 40. The mean is 20.5. The probabilities create a perfect bell curve. The standard deviation is 3.4. What is the probability of getting a number from 21 to 40?
• What is absolute deviation?
• How do you find a critical z value?
• The resting heart rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 15. How do you find the percentage of heart rates less than 85?
• Suppose that 40% of adult email users say "Yes." A polling firm contacts an SRS of 1500 people chosen from this population. If the sample were repeated many times, what would be the range of sample proportions who say "Yes"?
• 400 meters are normally distributed with a mean of 84 seconds and a standard deviation of 6 seconds. What percentage of the times are more than 72?
• Given a normal distribution with mean = 100 and standard deviation = 10, if you select a sample of n = 25, what is the probability that x-bar is between 95 and 97.5?
• Given a normal distribution with mean = 100 and standard deviation = 10, if you select a sample of n = 25, what is the probability that x-bar is above 102.2?
• For a standard normal distribution, what is the probability of obtaining a z value between -2.4 to -2.0?
• What is the special property of the standard normal distribution?
• In a standard normal distribution, what is the probability that Z is greater than 0.5?
• What is the 24th percentile of a normal population with a mean of 166 and a standard deviation of 68?
• How do you find the probability of #P( z< 1.45)# using the standard normal distribution?
• How do you find the probability of # P(-1.96 < z < 1.96)# using the standard normal distribution?
• How do you find the probability of # P(z < -2.58# or #z > 2.58)# using the standard normal distribution?
• How do you find the probability of # P(z < -1.96# or #z > 1.96)# using the standard normal distribution?
• How do you use the standard normal distribution to find #P(-2.25 < z < 1.25)#?
• For a standard normal distribution, how do you find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean?
• What percent of cases fall between the mean and one standard deviation above the mean?
• What percent of cases fall between the mean and –1 to +1 standard deviations from the mean?
• What percent of scores will fall between –3 and +3 standard deviations under the normal curve?
• In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value?
• What is the area under the standard normal probability distribution between z = 0 and z = 2.08?
• Let z be a random variable with a standard normal distribution. Find the indicated probability. What is the probability that P(−0.86 ≤ z ≤ 0)?
• Let z be a random variable with a standard normal distribution. Find the indicated probability. What is the probability that P(−0.61 ≤ z ≤ 2.50)?
• Let z be a random variable with a standard normal distribution. Find the indicated probability. What is the probability that P(z ≤ 1.18)?
• For the standard normal distribution, what is the probability of obtaining a z value greater than zero?
• In the standard normal distribution, how do you find the values of z for the 75th, 80th, and 92nd percentiles?
• Let #X ~ N(4, 16)#. How do you find #P(X < 6)#?
• Let #X ~ N(4, 16)#. How do you find #P(X > 0)#?
• Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected?
• If z is a standard normal random variable,what is the area between z = -1.20 and z = 1.40?
• Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. What percentage of scores is less than 140?
• Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. What is the percentage of scores greater than 120?
• Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. What is the percentage of scores between 80 and 120?
• Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. What is the percentage of scores between 80 and 140?
• The length of human pregnancies from conception to birth varies according to a distribution that is normal with mean 266 days and standard deviation 16 days. Between what values do the lengths of the middle 95% of all pregnancies fall?
• IQs are normally distributed with a mean of 100 and standard deviation of 16. How do you use the 68-95-99.7 rule to find the percentage of people with scores below 84?
• If students toss a coin 200 times each, about 68% should have proportions between what two numbers?
• Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(z > b)=0.9706#, what is #b#?
• Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(z > c)=0.0606#, how do you find #c#?
• Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(-d < z < d)=0.4844#, how do you find #d#?
• How do you find the z-scores that separate the middle 41% of the distribution from the tails of a standard normal distribution?
• How do you find the area under the standard normal curve for the z-score interval z < -1.6?
• What is #P(0.59 < z < 1.77)#?
• What is #P(z > 1.37) #?
• What is #P(z < −4.31)#?
• What is #P (Z>1.70)#?
• What is #P (Z< -2.12)#?
• What is #P (1.25<Z<2.06)#?
• What is the area under the standard normal curve between z = .84 and z = 1.95?
• What is the the area under the standard normal curve between z = -2.49 and z = -0.57?
• What is the area under the standard normal curve to the right of z = 1.43?
• How do you find #z# so that 82% of the standard normal curve lies to the right of #z#?
• How do you find the value of #z# so that the area under the standard normal curve from 0 to #z# is 0.4049?
• How do you find the area under the standard normal curve that lies to the right of z = 2.01?
• How do you find the area under the standard normal curve that lies between z = -1.00 and z = -1.10?
• What's the percentage of area under a normal curve between the mean and -.90 standard deviations below the mean?
• What is the area under the normal curve between z = -1.0 and z = -2.0?
• The time required to finish a test is normally distributed (i.e. in a Gaussian distribution) with a mean of 60 minutes and a standard deviation of 10 minutes. What is the probability that a student will finish the test in less than 70 minutes?
• The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. If 10,000 students take the exam, how many would you expect to score between 1700 and 1775 points?
• The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the probability that a student will finish the test between 50 and 60 minutes?
• The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. What is the z-score test result of 1800 points?
• The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the z-Score for a student who finishes the test in 45 minutes?
• The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. What is the probability that a student will score more than 1700 points?
• Let #X# be #N(mu, sigma^2)# so that #P(X<89) = 0.90# and #P(X<94) = 0.95#. How do you find #mu# and #sigma^2#?
• If the variance of the data values in a sample is 225, what is the standard deviation of the data values?
• Does the standard error of the mean show how close the sample mean is from the population mean?
• Assume that the random variable #X# is normally distributed, with mean = 50 and standard deviation = 7. How would I compute the probability #P( X > 35 )#?
• Given that #z# is a standard normal random variable, what is the value of #z# if the area to the right of #z# is 0.1112?
• Given that #z# is a standard normal random variable, what is the value of #z# if the area to the right of #z# is .1401?
• Given that #z# is a standard normal random variable, what is the value of #z# if the area between #-z# and #z# is .754?
• For normal distribution, what is the probability that an observation is within 1.33 standard deviations from the mean?
• If a woman between the ages 18-24 is randomly selected, what is the probability that her systolic blood pressure is greater than 110?
• In a standard normal distribution, what is the probability that #P(z<.45)#?
• In a standard normal distribution, what is the probability that #P(-.89<z<0)#?
• In a standard normal distribution, what is the probability that #P(z<-2.58# OR #z>2.58)#?
• What is the probability that a data value in a normal distribution is between a z-score of -.18 & 1.23?
• A student's commute to school is normally distributed with a mean of 31 min and a standard deviation of 6 min. What is the probability that the student gets to school in 19 to 31 min?
• What is value of #X# such that #P(-X < Z < X)=0.95#?
• Using the standard normal distribution, what is the probability #P(Z=7)#?
• If a set of grades on statistics examination are approximately normally distributed with a mean of 74 and a standard deviation of 7.9, what is the highest B if the top 5% of the students are given A's?
• If a set of grades on statistics examination are approximately normally distributed with a mean of 74 and a standard deviation of 7.9, what is the lowest B if the top 10% of the students are given A's and the next 25% are given B's?
• A banker finds that the number of times people use automated-teller machines in a year are normally distributed with a mean of 40.0 and a standard deviation of 11.4. What is the percentage of customers who use them less than 25 times?
• A banker finds that the number of times people use automated-teller machines in a year are normally distributed with a mean of 40.0 and a standard deviation of 11.4. What is the percentage of customers who use them more than 35 times?
• A banker finds that the number of times people use automated-teller machines in a year are normally distributed with a mean of 40.0 and a standard deviation of 11.4. What is the percentage of customers who use them between 45 and 55 times?
• Given the data -6, -9, -6, -4, 10, what is the z-score of 10?
• The mean number of seeds in a watermelon is 176 and the standard deviation is 40. What percentage of melons have between 150 and 200 seeds?
• The mean number of seeds in a watermelon is 176 and the standard deviation is 40. What percentage of melons have less than 100 or greater than 225 seeds?
• What percentage of the population values fall under 1.5 standard deviations in a normal distribution?
• Catfish weights are normally distributed with a mean of 3.2 pounds and a standard deviation of 0.8 pounds. What is the probability that a randomly selected catfish weighs between 3 and 4 pounds?
• The annual snowfall in a town has a mean of 38 inches and a standard deviation of 10 inches. Last year there were 63 inches of snow. How many standard deviations from the mean is that?
• Which is better: a score of 82 on a test with a mean of 70 and a standard deviation of 8, or a score of 82 on a test with a mean of 75 and a standard deviation of 4?
• Assume that the heights of women are normally distributed with a mean of 65.4 inches and a standard deviation of 2.3 inches. How do you find Q3?
• Assume adults have IQ that are normally distributed with a mean of 105 and standard deviation of 15. How do you find P(14), which is the score separating the bottom 4% from the top 96%?
• Human body temperatures are normally distributed with a mean of 98.6 and a standard deviation of 0.72.? How do I Find the temperature that separates the top 7% from the bottom 93%?
• Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(-e<z<e)=0.2128#, what is #e#?
• Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(z<b)=.9817#, what is #b#?
• Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If #P(z>c)=.0559#, what is #c#?
• A set of test scores is normally distributed with a mean of 78 and a standard deviation of 4.5. Dwayne scored 87 on the test. What is his percentile score?
• How do you make data normally distributed?
• A set of data has a normal distribution with a mean of 180 and a standard deviation of 20. What percent of the data is in the interval 140 - 220?
• The heights of women at a large university are approximately bell-shaped, with a mean of 65 inches and standard deviation of 2.5 inches. What is the probability that two randomly selected women are 62.5 inches or shorter?
• The heights of women at a large university are approximately bell-shaped, with a mean of 65 inches and standard deviation of 2.5 inches. What is the probability that two randomly selected women are 65 inches or taller?
• What percentage of the women in the researcher's sample would you expect to have a height of 68.5 inches or less?
• A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .03 significance level. What is the p-value?
• What is the the area under the normal distribution curve to the right of #z= -1.03#?
• How do you find the area under the standard normal distribution curve between z = 0 and z = 0.75?
• How do you find the area under the normal distribution curve to the right of z = –3.24?
• How do you find the area under the normal distribution curve to the right of z = –3.24?
• How do you find the area under the normal distribution curve between z = 1.52 and z = 2.43?
• How do you find the area under the standard normal curve that lies between z = 0 and z = 0.85?
• How do you find the area under the standard normal distribution curve between z = 1.65 and z = 2.51?
• What is the relationship between the normal curve and the standard deviation?
• What is a normal probability curve?
• What is the area under the normal distribution curve between z = 1.52 and z = 2.43?
• What is the fraction of the area under the normal curve between z = -0.87 and the mean?
• What is the fraction of the area under the normal curve between z = -0.87 and z = 1.62'?
• What is the fraction of the area under the normal curve between z = -1.91 and z = -0.62?
• What is the fraction of the area under the normal curve left of z = -2.12?
• What is the area under the standard normal curve between z = 0 and z = 3?
• Question #567c7
• The times it takes 5th graders to complete a mathematics problem are Normally distributed with mean 2 min and standard deviation 0.8 min. What is the probability that a randomly chosen 5th grader will take more than 2.5 minutes to complete the problem?
• The profit of a small and medium enterprise (SME) has a mean of #£46,000# and standard deviation of #£19,000#. What is the probability that profit of a SME will be between #£40,000# and #£50,000#?
• What proportion of the numbers are between 0 and 0.2 (normal distribution)?