Question

Math statistics, I need help on the red X “The speed of cars passing through the intersection of blossom hill and the Almaden expressway varies from 12 to 35 mph and is normally distributed. None of the cars trave more than 35 mph.” X~(12,35)

Answer 1

7967/10000

Explanations

Based on the information given, we have the following data:

`\begin{gathered} \mu=23.5\text{ (Mean)} \\ \sigma=6.64\text{ (Standard deviation)} \\ X=29mph \end{gathered}`

Convert the X-value to z-score using the formula:

`z=(X-\mu)/(\sigma)`

Substitute the given z-score into the formula:

`\begin{gathered} z=(29-23.5)/(6.64) \\ z=(5.5)/(6.64) \\ z=0.8283 \\ z\approx0.83 \end{gathered}`

Hence we need to find P(z ≤ 0.8283). Using the z-table, to get the equivalent probability

P(z ≤ 0.83) = 0.7967

P(z ≤ 0.83) ≈ 7967/10000

Hence the probability that the speed of the car is at most 29mph is 7967/10000