Question 4 (Mandatory) (3 points) Of the total population of the United States, 20% live in the northeast. If 200 residents of the United States are selected at random, find the probability that at least 50 live in the northeast. 0.0307 0.0465 0.0384 0.0475 0.0392 Question 5 (Mandatory) (3 points) The calcium levels in men and women ages 60 or older are summarized in the following table. mean standard deviation men 797 482 women 660 414 Use these estimates as the mean and standard deviation for the U.S. population for these age groups: If we take a random sample of 40 men and 35 women, what is the probability of obtaining a difference between sample means (men - women) of 105 or more? 0.6255 0.3745 0.6179 O 0.3783 0.6217 Question 6 (Mandatory) (3 points) A sample of 1500 people from a certain industrial community showed that 800 people suffered from a lung disease. A sample of 1000 people from a rural community showed that 300 suffered from the same lung disease. Assume these two proportions give good estimates of population proportions, respectively. Find the probability that the difference of the proportions (industrial - rural) is greater than 0.2 if two samples of size 150 and 100 are drawn from the two populations, respectively. 0.3121 O 0.7054 O0.2981 0.6019 0.3300