Question

For a set of shirt prices normally distributed with a mean of $45 and a standard deviation of $5, what is the probability that a randomly selected shirt is priced above $50?

a) 15.87%
b) 23.85%
c) 84.13%
d) 76.15%

Answer 1

Using the z-score and the standard normal distribution table, the probability that a randomly selected shirt is priced above $50 is found to be 15.87%, corresponding to option a).

Step-by-step explanation:

To find the probability that a randomly selected shirt is priced above $50, we will use the normal distribution properties. Since the mean price is $45 and the standard deviation is $5, we can calculate the z-score for a shirt priced at $50.

Z = (X - μ) / σ = ($50 - $45) / $5 = 1

Now we need to look at the standard normal distribution table to find the probability of z being less than 1, which gives us the area to the left of z. To find the probability of a shirt costing more than $50, we subtract this value from 1.

For z = 1, the area to the left of z is approximately 0.8413. Thus, the probability of a randomly selected shirt being priced above $50 is:

P(Z > 1) = 1 - P(Z < 1) = 1 - 0.8413 = 0.1587 or 15.87%

Therefore, the correct answer is a) 15.87%%.