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?

Expert's answer

a.

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

"-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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