Question

The space shuttle’s external tank holds cryogenic propellants. If the number of liters per tank lies along a normal curve with a mean of 2 million and a standard deviation of four hundred thousand (0.4 million), find the percentage of tanks which hold exactly 1.8 million liters.

Answer 1

Solution:

We are given

Variable follows normal distribution with

µ = 2 million

σ = 0.4 million

We have to find P(X=1.8)

So, by using approximation, we have

P(X=1.8) = P(1.8 - 0.5 < X < 1.8 + 0.5) = P(1.3 < X < 2.3)

P(1.3 < X < 2.3) = P(X < 2.3) - P(X < 1.3)

Find P(X < 2.3)

Z = (X - µ)/σ

Z = (2.3 - 2)/0.4

Z = 0.75

P(Z < 0.75) = P(X < 2.3) = 0.773373

(by using z-table)

Now, find P(X < 1.3)

Z = (X - µ)/σ

Z = (1.3 - 2)/0.4

Z = -1.75

P(Z < -1.75) = P(X < 1.3) = 0.040059

(by using z-table)

P(1.3 < X < 2.3) = P(X < 2.3) - P(X < 1.3)

P(1.3 < X < 2.3) = 0.773373 - 0.040059

P(1.3 < X < 2.3) = 0.733314

P(X=1.8) = 0.733314

Required probability = 0.733314