What percentage of the males in this age bracket could be expected to have a serum

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 4.111 A wildlife biologist is studying turtles that have been exposed to oil spills in the Gulf of Mexico. Previous studies have determined that a particular blood disorder occurs in turtles ex- posed for a length of time to oil at a rate of 1 in every 8 exposed turtles. The biologist examines 12 turtles exposed for a considerable period of time to oil. If the rate of occurrence of the blood disorder has not changed, what is the probability of each of the following events? She finds the disorder in:

a. none of the 12 turtles. b. at least 2 of the 12 turtles.

c. no more than 4 turtles. 4.112 Airlines overbook sell more tickets than there are seats flights, based on past records that indicate that approximately 5 of all passengers fail to arrive on time for their flight. Sup- pose a plane will hold 250 passengers, but the airline books 260 seats. What is the probability that at least one passenger will be bumped from the flight? 4.113 For the last 300 years, extensive records have been kept on volcanic activity in Japan. In 2002, there were five eruptions or instances of major seismic activity. From historical records, the mean number of eruptions or instances of major seismic activity is 2.4 per year. A researcher is interested in modeling the number of eruptions or major seismic activities over the 5-year period, 2005 –2010. a. What probability model might be appropriate? b. What is the expected number of eruptions or instances of major seismic activity during 2005 –2010?

c. What is the probability of no eruptions or instances of major seismic activities

during 2005 –2010?

d. What is the probability of at least two eruptions or instances of major seismic

activity? Text not available due to copyright restrictions