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
Expert's answer
2022-06-20T13:10:28-0400

a.


P(X5)=05112dx=512P(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=μx=\mu


μ=78+922=85\mu=\dfrac{78+92}{2}=85


P(78<X<92)=P(Z<9285σ)P(78<X<92)=P(Z<\dfrac{92-85}{\sigma})

P(Z7885σ)=P(Z<7σ)P(Z7σ)-P(Z\le\dfrac{78-85}{\sigma})=P(Z<\dfrac{7}{\sigma})-P(Z\le -\dfrac{7}{\sigma})

=0.95=0.95

P(Z7σ)=10.952P(Z\le -\dfrac{7}{\sigma})=\dfrac{1-0.95}{2}

7σ=1.96-\dfrac{7}{\sigma}=-1.96

σ=71.96\sigma=\dfrac{7}{1.96}

σ=3.57\sigma=3.57


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