This Qulz: 9 pts possib A trucking company delermined thait the distance travele

Question

This Qulz: 9 pts possib A trucking company delermined thait the distance traveled per truck per year is nomally distributed, with a mean of 70 thousand miles and a standard deviation of 12 thousand mies Complete parts (a) through (c) below a. What proportion of trucks can be expected to traval betwoon 56 and 70 thousand mles in a year? The proportion of trucks that can be expected to travel behwoon 55 and 70 thousand miles in a year is Round to four decimal places as reoded.) b. What percentage of trucks can be expected to travel ether less than 45 or more than 90 thousand miles in a year? The percentage of trucks that can be expected to travel either less han 45 or more than 90 thousand miles in a yoar is (Round to bwo decimal places as needed.) e, How many miles will betraveled by at least 99%of0°trucks? The amount of mies hat wil behavied by at least 90%ofte trucks i, L]mies. (Round to the nearest mile as needed) Enter your answer in each of the answer boxes Save for Later C aa-10-29-2017-11 MacBook Air 3 5 6 G H

Explanation / Answer

we are given that mean =70 and standard deviation=12

a. P(55<X<70)=P(X<70)-P(X<55)

=P(Z<70-70/12)-P(Z<55-70/12)

=P(Z<0)-P(Z<-1.25)

=0.5-0.10565=0.39435

b.

P(X<45)+P(X>90)=P(Z<-2.083)-[1-P(Z<1.666)]

=0.01862+0.04785

=0.06648

c.

P(x>z)=0.9

P(x<z)=0.1 so z=-1.28

x=mean-1.28*stnadard deviation

=77-1.28*12=61.64 miles

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