The distribution of all Indian River County grapefruit weights is known to be normally distributed with a mean of 303 grams and a standard deviation of 28 grams. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary.

Find the probability. that a random sample of 30 grapefruit has a mean weight less than 299 grams.

P(sampling distributions x < 299) = -----

Find the probability that a random sample of 30 grapefruit has a mean weight between 304 and 314 grams.

P(304 < sampling distribution x < 314) =

2- The distribution of the ages of all IRSC students is known to be normally distributed with a mean of 21.5 years and a standard deviation of 4.9 years. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary.

Find the probability that a random sample of 48 students has a mean age of greater than 22.5 years.

P(sampling distribution x > 22.5) = ----

Find the probability that a random sample has a mean age between 20.1 and 23.6 years.

P(20.1 < sampling distribution x < 23.6)

3- The standard deviation of the lifespan of a certain brand of LED light bulbs is 16 months. The quality control department at this company takes a random sample of 85 LED light bulbs and finds the mean lifespan of sample is 124 months. What is the probability that this sample mean is within 1 months of the mean of all light bulbs produced by the company? Round the solution to four decimal places, if necessary.

P(sampling distribution x within 1 months of mean) = -----

4- According to a recent Pew Research poll, 68% of American say that the U.S. economic system unfairly favors the powerful. In a recent sample of 620 Americans, 436 agreed that the U.S. economic system unfairly favors the powerful.

Determine the values of P and p^. Round to two decimal places, if necessary.

p = ---

p^ = ----