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Item 8Exercise 5-58
A manufacturer of computer chips claims that the probability of a defective chip is 0.005. The manufacturer sells chips in batches of 700 to major computer companies.
a. How many defective chips would you expect in a batch? (Round the final answer to 2 decimal places.)
Number of chips
b. What is the probability that none of the chips are defective in a batch? (Round the final answer to 4 decimal places.)
Probability
c. What is the probability at least one chip is defective in a batch? (Round the final answer to 4 decimal places.)
Probability
A company makes electric motors. The probability an electric motor is malfunctioning is 0.01. What is the probability that a sample of 300 electric motors will contain exactly 5 defective motors?
A marketing manager is in the process of deciding whether to introduce a new product. He has concluded that he needs to perform a market survey in which he asks a random sample of people whether they will buy the product. How large a sample should he take if he wants to estimate the proportion of people who will buy the product to within 3%, with 99% confidence?
Find n, given that we wish to estimate Mean to within 10 units, with 95% confidence, and assuming that Standard Deviation=100.
A random sample of 722 residents in a major town was asked whether they had ever been bitten by a dog. The responses (1=Yes and 2=N0) are recorded. Estimate with 95% confidence the proportion of residents who have been bitten by a dog.
Sample frequencies: n (1) = 304; n (2) = 418
Surveyors asked a random sample of women in a major city what factor was the most important in deciding where to shop. The results appear in the following table. If the sample size was 1200, estimate with 95% confidence the proportion of women who identified price and value as the most important factor.
Factor Percentage (%)
Price and Value 40
Quality and selection of merchandise 30
Service 15
Shopping environment 15
In a random sample of 500 observations, we found the proportion of successes to be 48%.
Estimate with 95% confidence the population proportion of successes.
a) Repeat part (a) with n=200.
b) Repeat part (a) with n = 1000.
c) Describe the effect on the confidence interval estimate of increasing the sample size.
A manufacturer of a brand of designer jeans realizes that many retailers charge less than the suggested retail price of $40. A random sample of 20 retailers reveals that the mean and the standard deviation of the prices of the jeans are $32 and $2.50 respectively. Estimate with 90% confidence the mean retail price of the jeans.
A survey of 20 Sri Lankan companies indicated that the average annual income of company secretaries was Rs.120 000. Assuming that the population standard deviation is Rs.7500 and that the annual incomes are normally distributed, calculate the 90% confidence interval estimate of the average annual income of all company secretaries.
A random sample of 25 was drawn from a normal distribution whose standard deviation is 5.
The sample mean was 80.
a) Determine the 95% confidence interval estimate of the population mean.
b) Repeat part (a) with a sample size of 100.
c) Repeat part (a) with a sample size of 400.
d) Describe what happens to the confidence interval estimate when the sample size increases.
