Question

Suppose that the speed at which cars go on the freeway is normally distributed with mean 73 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers

asked Jun 6, 2023 9.4k views

Suppose that the speed at which cars go on the freeway is normally distributed with mean 73 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(73Correct,9Correct) b. If one car is randomly chosen, find the probability that it is traveling more than 74 mph. 0.4558Correct c. If one of the cars is randomly chosen, find the probability that it is traveling between 72 and 76 mph. 0.17478Correct d. 69% of all cars travel at least how fast on the freeway? 68.5Incorrect mph.

Akash Kinwad asked

by Akash Kinwad

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Syam Kumar S · Answer 1 · 2023-06-11T09:46:43+0000

Answer:

68.536 mph

Explanation:

Part D

• Mean Speed = 73 mph

,

• Standard deviation = 9 mph.

Since we are supposed to find at least how fast on the freeway, then:

$\begin{gathered} P(X\geq x)=0.69 \\ 1-P(XFrom the z-table, the z-value at 31% is -0.496.[tex]\begin{gathered} z=(X-\mu)/(\sigma) \\ -0.496=(X-73)/(9) \\ \text{ Cross multiply} \\ X-73=9*-0.496 \\ X=73+(9*-0.496) \\ X=68.536 \end{gathered}$

69% of all cars travel at least 68.536 mph on the freeway.

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