Question

A variable of a population has a mean of ?=150 and a standard deviation of ?=21. a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean __ and standard deviation __

A company sells sunscreen in 500 milliliters (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean ?=497 ml and a standard deviation ?=5 ml. Suppose a store that sells this sunscreen advertises a sale for 5 tubes for the price of 4. Consider the average amount of lotion from an SRS of 5 tubes of sunscreen and find: (a) The standard deviation of the average, ?¯ : (b) The probability that the average amount of sunscreen from 5 tubes will be less than 489 ml. Answer:

Assume that women's weights are normally distributed with a mean given by ?=143 lb and a standard deviation given by ?=29 lb. (a) If 1 woman is randomly selected, find the probabity that her weight is between 113 lb and 179 lb (b) If 6 women are randomly selected, find the probability that they have a mean weight between 113 lb and 179 lb (c) If 63 women are randomly selected, find the probability that they have a mean weight between 113 lb and 179 lb

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 112 cm and a standard deviation of 4.8 cm. A. Find the probability that one selected subcomponent is longer than 114 cm. Probability = B. Find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 114 cm. Probability = C. Find the probability that if 3 are randomly selected, all 3 have lengths that exceed 114 cm. Probability =

Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112. (a) If 1 man is randomly selected, find the probability that his score is at least 587. (b) If 15 men are randomly selected, find the probability that their mean score is at least 587. 15 randomly selected men were given a review course before taking the SAT test. If their mean score is 587, is there strong evidence to support the claim that the course is actually effective?

Answer 1

Question: A variable of a population has a mean of ?=150 and a standard deviation of ?=21. a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean __ and standard deviation __

Answer: We know that if the repeated samples of size 49 taken from the population where population mean is 150 and the population standard deviation is 21 then is mean of all sample means is same as population mean and the standard deviation of all sample mean is given by ?/ (√ n). Therefore,

Mean of sample mean = 150

Standard deviation of sample means = ?/ (√ n) = 21/√49 = 21/7 = 3