uppose widget masses have a mean of 20 grams and a standard deviation of 5 grams. It is known that 5grams is the 84th percentile of the widget masses. A random sample of 500 widgets is taken. Find pproximate probabilities for each of the following: a. The average mass of the widgets in the random sample was greater than 20.1 grams. b. More than 100 of the widgets have mass more than 25 grams.

The box model we created for the cereal toys had a mean of 30 and a standard deviation of 12.25. What is the chance of the sum of 80 draws from this box being less than 2600?

An engineer is going to redesign an ejection seat for the airplane. The seat was designed for pilots weighing between 150 and 191 pounds. The new population of pilots has normally distributed weights with a mean of 158 pounds and a standard deviation or 31.1 pounds. a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 191 lb.  b. If 38 pilots are randomly selected, find the probability that their mean weight is between 150 lb and 191 lb. what is the approximate probability? c. When redesigning the ejection seat, which probability is more relevant? part b because the seat performance for a single pilot is more important part b because the seat performance for a sample of pilots is more important Part a because the seat performance for a single pilot is more important  part a because the seat performance for a sample of pilots is more important.  please show solving steps and if possible tell me how to also get these answers through excel…

Suppose that the number of points scored in a game comes from a normal population with an average of 12 points and a standard deviation of 9 points. Estimate the chance that the average points scored in ten randomly selected games will exceed 14.2 points. A. 0.4034 B. 0.0073 C. 0.2198 D. 0.2297