. a) The weight of white lab mice has a normal distribution. What is the mean and variance of white lab mice weight if it is known that 99.2% of the mice have a weight that is less than 171.15 rams and 12.1% have a weight that is above 152.55 grams? ) The weight of black lab mice has a normal distribution with mean of 140 grams and standard of 16 aroma What is the probability that domly com lod block migo there

An urn contains 7 black and 18 white balls. A ball is randomly drawn from the urn. Let X = 1 if a white ball is drawn and let X = -1 if a black ball is drawn. Find the following a) mean of X b) variance of X Please provide your working and round your answers to 2 decimal places

9. Women's heights are normally distributed with a mean of 63.8 in and standard deviation of 2.6 in. a) If one woman is randomly selected, find the probability that her height is less than 62.4 inches. b) If one woman is randomly selected, find the probability that her height is more than 64.5 inches. c) If one woman is randomly selected, find the probability that her height is between 61.0 inches and 68.0 inches. d) If 24 women are randomly selected, find the probability their mean height is less than 62.1 inches. e) Find P17.

The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of eleven students and nine faculty.​ (a) What is the probability of selecting a jury of all​ students? (b) What is the probability of selecting a jury of all​ faculty? (c) What is the probability of selecting a jury of three students and five ​faculty?

Suppose the weight of turkeys in a store are normally distributed with mean 15.5 lb and standard deviation 2 lb. If a turkey is grabbed at random what is the probability that the weight will be less than 16 lb?

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 137 lb and a standard deviation of 34.8 lb. if 35 different pilot are randomly selected find the probability that their mean weight is between 130 lb and 181 lb

The weights of all the turkeys sold in Fairfax County in 2020 were recorded in the data set “Fairfax Turkey Weights” found in the histogram. The weights are presented in pounds. There are 235,428 turkeys in this population. Calculate the probability that, in a random sample of eight turkeys, the mean weight is between 17 and 20 pounds. First, draw a picture with the rounded mean and values labeled and the shaded area representing the desired probability. Next, take a picture of your hand drawn sketch and upload it (if you do not have this technology, you may use any other method (i.e. Microsoft paint) to sketch the image). Then, complete this part by standardizing and using the Standard Normal Table to obtain this probability. Show your work “by hand”.

6. Frackly Oil is sold in 900 milliliter (ml) cans. The mean volume of oil placed in a can is 880 ml with a standard deviation of 7.8 ml. Assuming a normal distribution of the data, what is the probability that the filling machine will cause an overflow in a can, that is, the probability that more than 900 ml will be placed in the can?

If I roll two six-sided dice, what is the mean and variance of their difference? (note, the difference of 3 and 1 is 3 - 1 = 2, but the difference of 1 and 3 is 1-3 = -2) a) What is the mean? (express as an integer or reduced fraction) Reduce your answer to lowest terms. b) What is the variance? (express as an integer or reduced fraction) Reduce your answer to lowest terms. Submit part