At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years. If an employee is picked at random, what is the probability that the
Employee has worked at the store for over 10 years?
A) $49.16 \%$
B) $99.16 \%$
C) $0.84 \%$
D) $0.54 \%$

Question

At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years. If an employee is picked at random, what is the probability that the
Employee has worked at the store for over 10 years? 
A) $49.16 \%$
B) $99.16 \%$
C) $0.84 \%$
D) $0.54 \%$

Quizplus · Accepted Answer

We need to standardize the value of 10 years using the formula:

z = (x - μ) / σ

where
x = 10 years (value we want to find the probability for)
μ = 5.7 years (mean)
σ = 1.8 years (standard deviation)

z = (10 - 5.7) / 1.8
z = 2.38889 (rounded to 2.39)

Using a standard normal distribution table, the probability of getting a value greater than 2.39 is approximately 0.0084 or 0.84%. Therefore, the probability that an employee has worked at the store for over 10 years is 0.84%.

Choice C is the best answer.

At a Large Department Store, the Average Number of Years 49.16%49.16 \%49.16%

At a Large Department Store, the Average Number of Years $49.16 \%$