Chapter Test 291 Chapter Test 5 Take this test as you would take a test in class. 1. During a recent period of one year, the mean percent increase in value on Wednesdays of the cryptocurrency Dogecoin was 7.46%, with a standard deviation of 53.47%. Random samples of size 50 are drawn from this population and the mean of each sample is determined. (Source: Crypto Indicators) (a) Find the mean and standard deviation of the sampling distribution of sample means. (b) What is the probability that the mean percent increase for a given sample is more than 25%? (c) What is the probability that the mean percent increase for a given sample is between -10% and 30%? In Exercises 2–4, the random variable x is normally distributed with mean m = 18 and standard deviation s = 7.6. 2. Find each probability. (a) P1x 7 202 (b) P10 6 x 6 52 (c) P1x 6 9 or x 7 272 3. Find the value of x that has 88.3% of the distribution’s area to its left. 4. Find the value of x that has 64.8% of the distribution’s area to its right. In Exercises 5 and 6, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities. 5. A survey of U.S. undergraduates found that 37% of those attending in-state colleges would prefer to take a job in a different state after graduation. You randomly select 18 U.S. undergraduates attending in-state colleges. Find the probability that the number who would prefer to take a job in a different state after graduation is (a) exactly 7, (b) less than 5, and (c) at least 10. Identify any unusual events. Explain. (Source: College Pulse) 6. Fifty-nine percent of information technology (IT) professionals work for companies that rely on human memory to manage passwords. You randomly select 12 IT professionals. Find the probability that the number who work for companies that rely on human memory to manage passwords is (a) exactly 7, (b) more than 8, and (c) less than 4. Identify any unusual events. Explain. (Source: Yubico) The per capita disposable income for residents of a U.S. city in a recent year is normally distributed, with a mean of about $44,000 and a standard deviation of about $2450. Use this information in Exercises 7–10. 7. Find the probability that the disposable income of a resident is more than $45,000. Is this an unusual event? Explain. 8. Out of 800 residents, about how many would you expect to have a disposable income of between $40,000 and $42,000? 9. Between what two values does the middle 60% of disposable incomes lie? 10. Random samples of size 8 are drawn from the population and the mean of each sample is determined. Is the sampling distribution of sample means normally distributed? Explain.
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