A set of 5,000 on a college readiness exam are known to be approximately normally distributed with mean 72 and standard deviation 6. To the nearest integer value how many scores are there between 63 and 75?

1 Answer

Number of scores between 63 and 75 #color (red)(=3317)#

Explanation:

number in the set #=5000#
mean#=72#
standard deviation #sigma=6#

To compute for the probability #p# for normal distribution

#color(red)(p=int_(z_1)^(z_2) 1/sqrt(2pi)*e^(-0.5 z^2) dz)#

The actual class limits of 63 to 75 is 62.5 to 75.5

#z_1=(x_1-mu)/sigma=(62.5-72)/6=-19/12=-1.58333333#

#z_2=(x_2-mu)/sigma=(75.5-72)/6=7/12=0.58333333#

Compute now the probability #p#

#p=int_(z_1)^(z_2) 1/sqrt(2pi)*e^(-0.5 z^2) dz#

#p=int_(-1.58333333)^(0.58333333) 1/sqrt(2pi)*e^(-0.5 z^2) dz#

#p=0.6634927818#

Compute the number of scores between 63 and 75

#=p(5000)=0.6634927818(5000)=3317.463909~=3317#

God bless....I hope the explanation is useful.