In determining automobile mileage ratings, it was found that the mpg (X) for a certain model is normally distributed, with a mean of 32 mpg and a standard deviation of 1.3 mpg. Complete parts a through e below. a. Find P(X<31). P(X<31) = (Round to four decimal places as needed.) b. Find P(30 35). P(X>35)= d. Find P(X> 31). P(X>31)= (Round to four decimal places as needed.) e. Find the mileage rating that the upper 7% of cars achieve. The mileage rating that the upper 7% of cars achieve is mpg. (Round to two decimal places as needed.) (Round to four decimal places as needed.)

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**Understanding Normal Distribution in Automobile Mileage Ratings**

In determining automobile mileage ratings, it was found that the mpg (X) for a certain model is normally distributed, with a mean of 32 mpg and a standard deviation of 1.3 mpg. Complete parts a through e below.

**a. Find P(X < 31).**

\[ P(X < 31) = \_\_ \]  (Round to four decimal places as needed.)

**b. Find P(30 < X < 34).**

\[ P(30 < X < 34) = \_\_ \]  (Round to four decimal places as needed.)

**c. Find P(X > 35).**

\[ P(X > 35) = \_\_ \]  (Round to four decimal places as needed.)

**d. Find P(X > 31).**

\[ P(X > 31) = \_\_ \]  (Round to four decimal places as needed.)

**e. Find the mileage rating that the upper 7% of cars achieve.**

The mileage rating that the upper 7% of cars achieve is \[ \_\_ \] mpg. (Round to two decimal places as needed.)
Transcribed Image Text:**Understanding Normal Distribution in Automobile Mileage Ratings** In determining automobile mileage ratings, it was found that the mpg (X) for a certain model is normally distributed, with a mean of 32 mpg and a standard deviation of 1.3 mpg. Complete parts a through e below. **a. Find P(X < 31).** \[ P(X < 31) = \_\_ \] (Round to four decimal places as needed.) **b. Find P(30 < X < 34).** \[ P(30 < X < 34) = \_\_ \] (Round to four decimal places as needed.) **c. Find P(X > 35).** \[ P(X > 35) = \_\_ \] (Round to four decimal places as needed.) **d. Find P(X > 31).** \[ P(X > 31) = \_\_ \] (Round to four decimal places as needed.) **e. Find the mileage rating that the upper 7% of cars achieve.** The mileage rating that the upper 7% of cars achieve is \[ \_\_ \] mpg. (Round to two decimal places as needed.)
Expert Solution
Step 1: Determine the given information

For the given distribution of the milage (in mpg), it is given that:

The mean, μ=32.

The standard deviation, σ=1.3.

The distribution (defined to be distributed normally) of the milage rating is denoted as: X.


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