Question

The distribution of the runtimes of all movies is known to be skewed to the left with a mean of 96 minutes and a standard deviation of 14.67 minutes. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that a random sample of 51 movies has a mean runtime greater than 102.7 minutes. P(x > 102.7) Find the probability that a random sample of 51 movies has a mean runtime between 92 and 94.5 minutes. P(02<* 94.5)

Answer 1

To find the probability that a random sample of 51 movies has a mean runtime greater than 102.7 minutes, calculate the z-score and use a standard normal distribution table.

Step-by-step explanation:

To find the probability that a random sample of 51 movies has a mean runtime greater than 102.7 minutes, we need to calculate the z-score for 102.7 using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values, we get:

z = (102.7 - 96) / (14.67 / √51) = 1.76501

This z-score corresponds to a probability of approximately 0.0385 using a standard normal distribution table. Therefore, the probability that a random sample of 51 movies has a mean runtime greater than 102.7 minutes is approximately 0.0385.