Question

What proportion of the numbers are between 0 and 0.2 (normal distribution)?

17) Uniform Distribution The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform
probability distribution.

(a) Draw the graph of the uniform density function. Done
(b) What is the probability of generating a number between
0 and 0.2? Done
(c) What is the probability of generating a number between 0.25
and 0.6? Done
(d) What is the probability of generating a number greater than
0.95? Done
(e) Use your calculator or statistical software to randomly generate
200 numbers between 0 and 1. What proportion of the numbers
are between 0 and 0.2? Compare the result with part (b).

Answer 1

a)
b) `P(0\leX\le0.2)=0.2`
c) `P(0.25\leX\le0.6)=0.35`
d) `P(X\gt0.95)=0.05`
e) Answers vary

Explanation:

Why?

a) This is the uniform density function graph.
b) Based on the graph: `P(0\leX\le0.2)=b\cdoth=0.2\cdot1=0.2`
c) Based on the graph: `P(0.25\leX\le0.6)=b\cdoth=(0.6-0.25)(1)=(0.35)(1)=0.35`
d) Based on the graph: `P(x\gt0.95)=P(1-0.95)\rArrb\cdoth=0.05\cdot1=0.05`
e) in comments