Question

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. If a simple random sample of four tanks is selected, and their capacities can be considered independent, what is the probability that all four will hold between 14.75 and 15.10 gallons of gas?

Answer 1

Answer:  0.9084

Step-by-step explanation:

Given : The actual capacity of a randomly selected tank has a distribution that is approximately Normal with $\mu=15$

$\sigma=0.15$

Sample size : n=4

Using $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$ , for x= 14.75 , we have

$z=\dfrac{14.75-15}{\dfrac{0.15}{\sqrt{4}}}=-3.33333$

For x= 15.10 , $z=\dfrac{15.10-15}{\dfrac{0.15}{\sqrt{4}}}=1.33333$

Using standard normal z-value table,

P-value $= P(-3.3333<z<1.33333)=$

$P(z<1.33)-P(z<-3.33)=0.9087882-0.0004291=0.9083591\approx0.9084$

Hence, the probability that all four will hold between 14.75 and 15.10 gallons of gas = 0.9084