Statistics and Probability Answers

It is known from the medical records of millions of men from a large metropolis that the heights of grown men in this city follow a normal distribution with average height being 170.2 cm and 68% of men having a height between 162.6 cm and 177.8 cm. (a) If a random man is picked from this population, what is the probability that their height is more than 177.8 cm? (b) If a random sample of 9 men is picked, what is the probability that the mean height of men in this sample is more than 177.8 cm? What is the probability that the mean height of men in this sample is more than 174 cm? (c) Again, for a randomly chosen sample of 9 men, what is the probability that the mean height of the men in this sample is between 167.7 cm and 171.5 cm (d) If a large number of such random samples of 9 men are picked, what is the number such that 25% of these samples will have average height less than this number? (e) How does this number in the last part changes if the sample size is changed to 100 men in each sample? 

It is known that the monthly income of salaried persons in a large city are normally distributed with a standard deviation of 3600 Rs.. (a) A random sample of 9 individuals from this population is taken and it is found that their salaries are as follows: 44000, 41000, 43000, 42500, 43500, 41500, 41000, 46500, 35000 What is the probability that the average salary of the whole salaried population in the city lies somewhere between 40025 and 43975? 

A sample of 50 socks is taken. What is the probability that the mean length of the sample is shorter than 18 cm?

A sock producer is interested in how uniform the length of socks that are produced at his factory is. It is known that the sock length follows a normal distribution with a mean of 20 cm and a standard deviation of 10.5 cm.

The applicant to a company took a 60 item entrance exam. Their scores resemble a normal distribution with a mean of 50 and a standard deviation of 4. If the company would like to have the top 20 percent of the applicant to go on to the next phase of the application process, what should be their cut-off score in exam?

bank accepts thirty percent of loan requests from farmers. Ten loan requests from framers are randomly selected for consideration by the bank. Find the probability

if a population has a standard deviation of 20, what is the standard error of the mean if the sample size 16 is selected? 

a group of students got the following scores in an achievement test:9,12,15,18,21,and 24.consider sample of size 3 that can be drawn from this population

Find p^ and q^ X = 28 n = 110

25. Suppose that in Bangladesh, three accidents occur in different factories per year on average. a. What is the probability of no accidents during a one-year period? 

b. What is the probability of at least two accidents during a one-year period? c. What is the probability of no accidents during the next six months?