A fair coin is flipped 80 times and the number of heads that occur is noted. A random variable x is defined as the number of heads. Find the expected value, variance, and standard deviation

Americans spend an average 12.2 minutes in the shower. If the standard deviation of the variable is 2 minutes and the variable is normally distributed, find the probability that the mean time of a sample of 15 Americans who shower will be less than 12 minutes.

Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews representa random set of reviews. Find the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs. (a) Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability. ↑ 2.8 4 3.2 6.4 O 0.4 1.6 2.8 4 5.2 6.4 7.6 0.4 1.6 2.8 4 5.2 6.4 7.6 X O 0.4 1.6 0.4 1.6 WebAsign Plot 7.6 6.4 7.6 X (b) Give the probability statement and the probability. (Enter exact numbers as integers, fractions, or decimals for the probability statement. Round the…

The weights of steers in a herd are distributed normally. The variance is 40,000and the mean steer weight is 1000lbs. Find the probability that the weight of a randomly selected steer is greater than 600⁢lbs. Round your answer to four decimal places.