Question

Your pickle company rates its pickles on a scale of spiciness from 1 to 12. Market research shows that customer preferences for spiciness are normaliy distributed, with a mean of 6.5 and a standard deviation of 1. Assuming that you sell 60,000 jars of pickes, how many jars with a spiciness of 9 or above do you expect to selt?

Answer 1

To estimate the number of jars with a spiciness of 9 or above that you expect to sell, you can use the standard normal distribution and the z-score. Multiply the probability from the z-score table by the total number of jars sold to get the expected number of jars with a spiciness level of 9 or above.

Step-by-step explanation:

To find the number of jars with a spiciness of 9 or above that you expect to sell, you first need to convert the normal distribution to the standard normal distribution. You do this by subtracting the mean and dividing by the standard deviation. So for a spiciness level of 9, the z-score is (9 - 6.5) / 1 = 2.5. Using a z-table, you can find the area under the standard normal curve to the right of a z-score of 2.5. This area represents the probability that a randomly selected jar has a spiciness level of 9 or above.

Assuming a normal distribution, this probability can be used to estimate the number of jars with a spiciness level of 9 or above out of the 60,000 jars sold. You multiply the probability by 60,000 to get the expected number of jars sold with a spiciness level of 9 or above.

Note that this is an estimation based on the assumption of a normal distribution. The actual number of jars sold with a spiciness level of 9 or above may vary.