A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 30 thousand miles and a standard deviation of 11 thousand miles. Complete parts (a) through (d) below. The percentage of trucks that can be expected to travel either less than 15 or more than 40 thousand miles in a year is 26.80 %. (Round to two decimal places as needed.) c. How many miles will be traveled by at least 80% of the trucks? The number of miles that will be traveled by at least 80% of the trucks is 20,742 miles. (Round to the nearest mile as needed.) d. What are your answers to parts (a) through (c) if the standard deviation is 7 thousand miles? If the standard deviation is 7 thousand miles, the proportion of trucks that can be expected to travel between 17 and 30 thousand miles in a year is 0.4684. (Round to four decimal places as needed.) If the standard deviation is 7 thousand miles, the percentage of trucks that can be expected to travel either less than 15 or more than 40 thousand miles in a year is 9.26 %. (Round to two decimal places as needed.) If the standard deviation is 7 thousand miles, the number of miles that will be traveled by at least 80% of the trucks is (Round to the nearest mile as needed.) miles.

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How to calculate the third question of section (d). I need to understand step  by step.

Especially how to find the Z value 

Using the formula X= u + Zo

A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 30 thousand miles and a standard deviation of 11 thousand miles. Complete parts (a) through (d)
below.
The percentage of trucks that can be expected to travel either less than 15 or more than 40 thousand miles in a year is 26.80 %.
(Round to two decimal places as needed.)
c. How many miles will be traveled by at least 80% of the trucks?
The number of miles that will be traveled by at least 80% of the trucks is 20,742 miles.
(Round to the nearest mile as needed.)
d. What are your answers to parts (a) through (c) if the standard deviation is 7 thousand miles?
If the standard deviation is 7 thousand miles, the proportion of trucks that can be expected to travel between 17 and 30 thousand miles in a year is 0.4684'.
(Round to four decimal places as needed.)
If the standard deviation is 7 thousand miles, the percentage of trucks that can be expected to travel either less than 15 or more than 40 thousand miles in a year is 9.26 %.
(Round to two decimal places as needed.)
If the standard deviation is 7 thousand miles, the number of miles that will be traveled by at least 80% of the trucks is
miles.
(Round to the nearest mile as needed.)
Transcribed Image Text:A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 30 thousand miles and a standard deviation of 11 thousand miles. Complete parts (a) through (d) below. The percentage of trucks that can be expected to travel either less than 15 or more than 40 thousand miles in a year is 26.80 %. (Round to two decimal places as needed.) c. How many miles will be traveled by at least 80% of the trucks? The number of miles that will be traveled by at least 80% of the trucks is 20,742 miles. (Round to the nearest mile as needed.) d. What are your answers to parts (a) through (c) if the standard deviation is 7 thousand miles? If the standard deviation is 7 thousand miles, the proportion of trucks that can be expected to travel between 17 and 30 thousand miles in a year is 0.4684'. (Round to four decimal places as needed.) If the standard deviation is 7 thousand miles, the percentage of trucks that can be expected to travel either less than 15 or more than 40 thousand miles in a year is 9.26 %. (Round to two decimal places as needed.) If the standard deviation is 7 thousand miles, the number of miles that will be traveled by at least 80% of the trucks is miles. (Round to the nearest mile as needed.)
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