Please see the questions below:

Question 2 (10 points). NASA received 500 job applications during the last months. The HR team is planning to invite 200 of them for an interview. a. What is the probability that a simple random sample of 20 applicants will provide an estimate of the population proportion of applicant desiring on-campus housing that is within plus or minus .05 of the actual population proportion? (4 points) b. Discuss the selection of standard deviation formula used. (3 points) c. Discuss how would your results change if you decreased the sample size to 17. (3 points) .00 .01 .02 .03 .04 .05 06 .07 .08 .09 5000 5040 .5080 5120 5160 5199 .5239 .5279 .5319 5359 1 5398 5438 .5478 5517 5557 5596 .5636 .5675 5714 .5753 .2 .5793 .5832 .5871 .5910 5948 .5987 .6026 .6064 6103 .6141 3 .6179 6217 .6255 6293 6331 6368 .6406 .6443 .6480 .6517 4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 6915 6950 .6985 .7019 .7054 7088 .7123 .7157 7190 .7224 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 .7 .7580 7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 7852 8 .7881 .7910 .7939 .7967 .7995 8023 .8051 .8078 8106 .8133 9 .8159 8186 .8212 .8238 8264 .8289 .8315 .8340 .8365 .8389 Question 3 (5 points). In a village, power cuts occur randomly at a rate of 4 per year. a. Find the probability that in any given year there will be exactly 3 power cuts. (4 points) b. Find the probability that in any given year there will be no more than 1 power cuts. (4 points) c. Find the variance power cuts during the given 1 year. (2 points)