Answer:
Step-by-step 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
