Mimi is into figure skating these days due to the Winter Olympics. She started learning toe loop jumps a couple weeks ago. Her probability of landing a successful single toe loop jump is 0.30. She plans to attempt 10 single toe loop jumps in her practice session tomorrow.
(a) Let X be the number of successful single toe loop jumps that Mimi lands. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?
(b) Find the probability that Mimi lands at least one successful single toe loop jump in her 10 attempts. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.
Assume the weights of men are normally distributed with a mean of 170 lbs and a standard deviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Find the 75th percentile for the distribution of men's weights.
(b) What is the probability that a randomly selected man weighs more than 200 lbs?
Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100. Show all work. Just the answer, without supporting work, will receive no credit.
(a) If a random sample of 64 test scores is selected, what is the standard deviation of the sample mean?
(b) What is the probability that 64 randomly selected test scores will have a mean test score that is between 475 and 525?