The distribution of red blood cell counts is different for men and women in a certain population. For both, the distribution is approximately Normal. For men, the middle 95% range from 4.4 to 6.0 million celisper microliter, and for women, the middle 95% have red blood cell counts between 4.3 and 5.1 million cells per microliter. Complete parts (a) and (b) below a. What is the mean for the men? Explain your reasoning. Select the correct choice below and fill in the answer box to complete your choice. Round to two decimal places as needed.) O A. The mean is million. Since the Normal distribution is symmetric about its mean, the mean is O B. The mean is million. Since the mode of the Normal distribution is equal to its mean, the O C. The mean is million. Since the mode of the Normal distribution is equal to its mean, the the lower of the boundary values for the middle 95%. mean is the higher of the boundary values for the middle 95%. mean is equal to the distance between the boundary values for the middle 95%. right in the middle, which is the average of the boundary values for the middle 95%. O D. The mean ismillion. Since the Normal distribution is symmetric about its mean, the mean is b. Find the standard deviation for the men. Explain your reasoning. The standard deviation is million. The Empirical Rule states that about 95%ofthe data fall within deviation(s). The standard deviation is found by dividing the range of the middle 95% by 1 standard deviation(s) of the mean. The middle 95% of values spans | | standard Round to two decimal places as needed.)

a) Since the distribution is normal, the distance from the mean to the upper limit is going to be the same as the distance from the mean to the lower limit. The mean is going to be the mid point between the limits, which is going to be the average of the limits. The limits are going to have a z score associated, in this case the upper z is 1.96 and the lower z is -1.96 as shown in the picture.

(4.4 + 6.0)/2 = 5.2

The mean for men is going to be 5.2 million cells/uL

b) The standard deviation for men can be calculated using the z score and the limit values. The formula is shown in the picture.

σ = (6.0 - 5.2)/1.96 = 0.4

The standard deviation is 0.4 million cells/uL