Does it appear that the 45 data values appear to be a random sample from a normal

b. What percentage of the males could be expected to have serum cholesterol levels

within the clinical normal range of 150 –250 mgml?

c. If levels above 300 mgml are considered very risky, what percentage of the adult

males in this age bracket could be expected to exceed 300? Bus. 4.102 Marketing analysts have determined that a particular advertising campaign should make at least 20 of the adult population aware of the advertised product. After a recent cam- paign, 25 of 400 adults sampled indicated that they had seen the ad and were aware of the new product.

a. Find the approximate probability of observing y ⱕ 25 given that 20 of the popula-

tion is aware of the product through the campaign. b. Based on your answer to part a, does it appear the ad was successful? Explain. Med. 4.103 One or more specific, minor birth defects occurs with probability .0001 that is, 1 in 10,000 births. If 20,000 babies are born in a given geographic area in a given year, can we calculate the probability of observing at least one of the minor defects using the binomial or normal approxi- mation to the binomial? Explain. 4.104 The sample mean to be calculated from a random sample of size n ⫽ 4 from a popu- lation consists of the eight measurements 2, 6, 9, 12, 25, 29, 39, 50. Find the sampling distri- bution of . Hint: There are 70 samples of size 4 when sampling from a population of eight measurements. 4.105 Plot the sampling distribution of from Exercise 4.104. a. Does the sampling distribution appear to be approximately normal? b. Verify that the mean of the sampling distribution of equals the mean of the eight population values. 4.106 Refer to Exercise 4.104. Use the same population to find the sampling distribution for the sample median based on samples of size n ⫽ 4. 4.107 Plot the sampling distribution of the sample median of Exercise 4.119. a. Does the sampling distribution appear to be approximately normal?

b. Compute the mean of the sampling distribution of the sample median and compare

this value to the population median. 4.108 Random samples of size 5, 20, and 80 are drawn from a population with mean m ⫽ 100 and standard deviation s ⫽ 15.

a. Give the mean of the sampling distribution of for each of the sample sizes 5, 20,

and 80.

b. Give the standard deviation of the sampling distribution of for each of the sample

sizes 5, 20, and 80.

c. Based on the results obtained in parts a and b, what do you conclude about

the accuracy of using the sample mean as an estimate of population mean m? 4.109 Refer to Exercise 4.108. To evaluate how accurately the sample mean estimates the population mean m, we need to know the chance of obtaining a value of that is far from m. Sup- pose it is important that the sample mean is within 5 units of the population mean m. Find the following probabilities for each of the three sample sizes and comment on the accuracy of using to estimate m.

a. b.

c. 4.110 Suppose the probability that a major earthquake occurs on a given day in Fresno, California, is 1 in 10,000.

a. In the next 1,000 days, what is the expected number of major earthquakes in

Fresno?

b. If the occurrence of major earthquakes can be modeled by the Poisson distribution,

calculate the probability that there will be at least one major earthquake in Fresno during the next 1,000 days. P95 ⱕ y ⱕ 105 P y ⱕ 95 P y ⱖ 105 y y y y y y y y y y