Question

A luxury passenger liner has 500 passengers on board whose ages are normally distributed around a mean of 60 years with a standard deviation of 12 years. What is the probability of passengers less than 55 years old?

Answer 1

To find the probability of passengers less than 55 years old, we need to calculate the z-score for an age of 55 years using the formula:

z = (x - μ) / σ

Where:
x = 55 (the age we are interested in)
μ = 60 (mean)
σ = 12 (standard deviation)

Plugging in the values:

z = (55 - 60) / 12
z = -5 / 12
z = -0.4167

Next, we find the corresponding probability using a standard normal distribution table or a calculator. The probability of a z-score of -0.4167 or less can be found to be approximately 0.3372.

Therefore, the probability of passengers less than 55 years old is approximately 0.3372 or 33.72%.