# Answer to Question #351020 in Statistics and Probability for lei

Question #351020

the time between busses on stevens creek blvd is 12 minutes. Therefore the wait time of a passenger who arrives randomly at a bus stop is uniformly distributed between 0 and 12 minutes.

a. find the probability that a person randomly arriving at the bus stop to wait for the bus has a wait time of at most 5 minutes.

in the accompanying diagram, the shaded area represents approximately 95% of the scores on a standardized test. If these scores ranged from 78 to 92,

a. what is the mean?

b. what is the standard deviation?

1
2022-06-20T13:10:28-0400

a.

"P(X\\le 5)=\\displaystyle\\int_{0}^{5}\\dfrac{1}{12}dx=\\dfrac{5}{12}"

b. The shaded area is symmetric with respect the line "x=\\mu"

"\\mu=\\dfrac{78+92}{2}=85"

"P(78<X<92)=P(Z<\\dfrac{92-85}{\\sigma})"

"-P(Z\\le\\dfrac{78-85}{\\sigma})=P(Z<\\dfrac{7}{\\sigma})-P(Z\\le -\\dfrac{7}{\\sigma})"

"=0.95"

"P(Z\\le -\\dfrac{7}{\\sigma})=\\dfrac{1-0.95}{2}"

"-\\dfrac{7}{\\sigma}=-1.96"

"\\sigma=\\dfrac{7}{1.96}"

"\\sigma=3.57"

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