For any true/false if the statement is true or false explain why. It is impossible to get a z-score of 155. TRUE FALSE A new line of cars has gas mileage represented by a distribution that is approximately normal with a mean of 32 mpg and a standard deviation of 4 mpg. Use the empirical rule to answer the following: a)Approximately what percent of cars get between 24 and 32 mpg? b) Approximately what proportion of cars get between 28 and 40 mpg?

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For any true/false if the statement is true or false explain why.

  1. It is impossible to get a z-score of 155. TRUE FALSE

  2. A new line of cars has gas mileage represented by a distribution that is approximately normal with a mean of 32 mpg and a standard deviation of 4 mpg. Use the empirical rule to answer the following:

    a)Approximately what percent of cars get between 24 and 32 mpg?
    b) Approximately what proportion of cars get between 28 and 40 mpg?

Expert Solution
Step 1

1. FALSE

It is possible to get a value of 155. This would mean that the value would be present 155 times standard deviation from the mean. Since it is a high value, there is every chance that the value in question is an outlier.

2. Let X denote the gas mileage.

X~N32,16

a). To calculate P[24<X<32]

     P24<X<32=P24-324<X-324<32-324=P-2<Z<0=ϕ0-ϕ-2=0.47725

Therefore, the required percentage is 47.725%.

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