Question

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons. What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?

Answer 1

Answer:

0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.                                  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4000 gallons

Standard Deviation, σ = 125 gallons

Sample size, n = 40

We are given that the distribution of amount of fuel is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Central limit theorem:

As the sample size increases, the distribution of sample mean has a similar popular distribution shape.

P(sample of 40 jumbo jets will be less than 3950 gallons)

P(x < 3950)

$P( x < 3950) = P( z < \displaystyle\frac{3950 - 4000}{125}) = P(z < -0.4)$

Calculation the value from standard normal z table, we have,  

$P(x < 3950) = 0.6554 = 65.54\%$

0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.