Question

Use technology to solve the following problem: A ferry will safely accommodate 79 tons of passenger cars. Assume that the mean weight of a passenger car is 1.9 tons with standard deviation 0.5 tons. If a random sample of 39 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded

Answer 1

0.05155 or 5.155%

Explanation:

We are given;

Weight of passenger cars the ferry can accommodate = 79 tons of passenger cars

Number of cars loaded = 39

Thus;

population mean weight; μ = 1.9

Since it can accommodate 79 tons of passenger cars, then their average weight should not exceed;

79/39 = 2.03 thus;

Sample mean; x¯ = 2.03

Standard deviation; σ = 0.5

Sample size; n = 39

Let's find the z-score value;

z = (x¯ - μ)/(σ/√n)

Thus;

z = (2.03 - 1.9)/(0.5/√39)

z = 0.13/0.08

z ≈ 1.63

Thus; P(z > 1.63) = 1 - P(z < 1.63)

From the z-score table attached, the p-value which is the probability is P(z < 1.63)

Thus;

P = 1 - 0.94845

P = 0.05155 or 5.155%