Provide answers to the three part question about gasoline tanks. 7) Suppose the

Question

Provide answers to the three part question about gasoline tanks.

7) Suppose the actual capacity of randomly selected gasoline tanks from a certain type of vehicle is approximately normally distributed with mean of 12.0 gal and standard deviation of 0.78 gal. a) What is the probability that a randomly selected tank will hold at most 12.8 gal? b) What is the probability that a randomly selected tank will hold between 11.5 and 12.1 gal? c) Find the number of gallons that represents the 30th percentile

Explanation / Answer

Sol:

P(X<=12.8)

mean=12

sd=0.78

z=x-mean/sd

=12.8-12/0.78

=1.025

P(Z<1.025)

use rcode to find the probability

pnorm(1.025)

answer:0.8473184

the probbaility that a randomly selected tank will hold atmost 12.8 gal is 0.8473184

Solutionb:

P(11.5<X<12.1)

P(11.5-12/0.78<Z<12.1-12/0.78)

P(-0.64<Z<0.13)

P(Z<0.13)-P(Z<-0.64)

pnorm(0.13)-(1-pnom(0.64))

=0.2906

ANSWER:0.2906

Solutionc:

z score for 30 percentile is

z=-0.524

Z=x-mean/sd

-0.524=X-12/0.78

X=-0.524*0.78+12

X=12.40872

NO OF GALLONS THAT REPRESENT 30 TH PERCENTILE IS 12.41

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