The distribution of the runtimes of all movies is known to be skewed to the left with a mean of 117 minutes and a standard deviation of 14.76 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 38 movies has a mean runtime greater than 122.7 minutes.

P(sampling distribution x > 122.7) =----

Find the probability that a random sample of 38 movies has a mean runtime between 118.8 and 123.8 minutes.

P(118.8 < sampling distribution x < 123.8) = ---

2- A population of values has a normal distribution with mean = 49.1 and standard deviation = 8.9. You intend to draw a random sample size n = 165. Determine the standard deviation of the sampling distribution of x. Round solution to four decimal places, if necessary.

Standard deviation x = ---

3- Suppose there exists a population where 31% of its members possess a certain characteristic. Let p^ be the proportion of a random sample of 174 members that also possess that certain characteristic. Determine the following probability. Round solution to four decimal places, if necessary.

Find the probability that the sample proportion is between 0.24 and 0.3.

P(0.24 < p^ < 0.3) =