Question

The time to deliver a pizza is normally distributed with mean 22 minutes and standard deviation 7 minutes. During 1000 deliveries, in 52 cases the pizzas were delivered in less than x minutes. Find x. Give your answer to the nearest integer?

Answer 1

To find x, we need to calculate the z-score corresponding to the number of cases where the pizzas were delivered in less than x minutes. We can use the z-score formula: z = (x - mean) / standard deviation. Rearranging the formula, we have x = z * standard deviation + mean. Since we want to find x to the nearest integer, we can use the standard normal distribution table or calculator to find the z-score corresponding to the cumulative probability of 52 cases out of 1000 deliveries. Once we have the z-score, we can substitute it into the formula to find x.

Step-by-step explanation:

To find x, we need to calculate the z-score corresponding to the number of cases where the pizzas were delivered in less than x minutes. We can use the z-score formula: z = (x - mean) / standard deviation. Rearranging the formula, we have x = z * standard deviation + mean.

Since we want to find x to the nearest integer, we can use the standard normal distribution table or calculator to find the z-score corresponding to the cumulative probability of 52 cases out of 1000 deliveries. Once we have the z-score, we can substitute it into the formula to find x.