Complete Question
An airliner carries 300 passengers and has doors with a height of 75 inches. Heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. (Round to four decimal places as needed.)
Answer:
0.9839
Explanation:
We solve using formula Z score
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
We are to find thethe probability that he can fit through the doorway without bending. This means his height is less than (< ) the height of the doorway(75 inches).
z = 75 - 69/2.8
z = 2.14286
Probability value from Z-Table:
P(x ≤ 75) = P(x = 75) = P(x < 75)
= 0.98394
Approximately ≈ 0.9839