Question

The height of players on a football team is normally distributed with a mean of 74 inches, and a standard deviation of 1 inch. If there are 50 football players on the team, how many are less than 74 inches tall?

Answer 1

Explanation:

Let x be the random variable representing the height of players on the football team. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

n = number of samples

From the information given,

µ = 74 inches

σ = 1 inch

n = 50

x = 74 inches

the probability that a player is less than 74 inches tall is expressed as

P(x < 74)

For x = 74,

z = (74 - 74)/(1/√50) = 0

Looking at the normal distribution table, the probability corresponding to the z score is 0.5

Therefore,

P(x < 74)

The players less than 74 inches is

0.5 × 50 = 25 players