Question

The distribution of ages of licensed drivers shopping at the Kalish County Mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth.

a. What is the probability that the person is 48 or older?

b. What is the probability that the person is 48 or younger?

c. What is the probability that the person is between 41 and 48?

d. What is the probability that the person selected will be less than 27 years old?

1. a. The probability that the person is 48 or older is 0.8413.
This can be calculated using the standard normal cumulative distribution function as follows:
P(x ≥ 48) = 1 – P(x < 48) = 1 – 0.8413 = 0.8413
b. The probability that the person is 48 or younger is 0.8413.
This can be calculated using the standard normal cumulative distribution function as follows:
P(x ≤ 48) = P(x < 48) = 0.8413
c. The probability that the person is between 41 and 48 is 0.5199.
This can be calculated using the standard normal cumulative distribution function as follows:
P(41 ≤ x ≤ 48) = P(x ≤ 48) – P(x < 41) = 0.8413 – 0.3214 = 0.5199
d. The probability that the person selected will be less than 27 years old is 0.0013.
This can be calculated using the standard normal cumulative distribution function as follows:
P(x < 27) = P(x < 27) = 0.0013
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