Question

Data shows that a shop sells 500 pairs of glasses per week on average, with a standard deviation of 50. What is the probability that the shop will sell more than 600 pairs of glasses next week?

a. 2.28%
b. 4.57%
c. 31%
d. 42.28%

Answer 1

Using the Z-score for a value of 600 and a mean of 500 with a standard deviation of 50, we find that the probability of the shop selling more than 600 pairs of glasses next week is 2.28%, which corresponds to answer choice a.

Step-by-step explanation:

To determine the probability that the shop will sell more than 600 pairs of glasses next week, we must use the concept of normal distribution because the average and standard deviation are given. The Z-score formula will help us find how many standard deviations away from the mean 600 is. The Z-score is calculated as:

Z = (X - μ) / σ

Where:

• X is the value for which we are finding the probability (600 pairs)
• μ is the mean (500 pairs)
• σ is the standard deviation (50 pairs)

Z = (600 - 500) / 50

Z = 100 / 50

Z = 2

Using the Z-table, a Z-score of 2 gives a probability of about 0.9772 (97.72%) that a data point falls below 600. So, to find the probability of selling more than 600 pairs, we subtract this from 1:

P(X > 600) = 1 - P(Z < 2)

P(X > 600) = 1 - 0.9772

P(X > 600) = 0.0228

Therefore, the probability is 0.0228 or 2.28%, which corresponds to answer choice a.