Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 40, with a standard deviation of 28. A pollster draws a sample of 90 people to interview. (a) What is the probability that the sample mean income is less than 38? Round the answer to at least four decimal places. (b) What is the probability that the sample mean income is between 38 and 46? Round the answer to at least four decimal places. (c) Find the 40th percentile of the sample mean. Round the answer to at least one decimal place. (d) Would it be unusual for the sample mean to be less than 38? Round the answer to at least four decimal places. (e) Do you think it would be unusual for an individual to have an income of less than 38? Explain. Assume the population is approximately normal. Round the answer to at least four decimal places.
Added by William J.
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We can use the Central Limit Theorem, which states that the distribution of sample means will be approximately normal with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample Show more…
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Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 40, with a standard deviation of 28. A pollster draws a sample of 90 people to interview. a) What is the probability that the sample mean income is less than 38? Round the answer to at least four decimal places. (b) What is the probability that the sample mean income is between 38 and 46? Round the answer to at least four decimal places. (c) Find the 40th percentile of the sample mean. Round the answer to at least one decimal place. (d) Would it be unusual for the sample mean to be less than 38? Round the answer to at least four decimal places. (e) Do you think it would be unusual for an individual to have an income of less than 38? Explain. Assume the population is approximately normal. Round the answer to at least four decimal places.
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Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 43, with a standard deviation of 23. A pollster draws a sample of 91 people to interview. (a) What is the probability that the sample mean income is less than 40? Round the answer to at least four decimal places. The probability that the sample mean income is less than 40 is . (b) What is the probability that the sample mean income is between 41 and 44? Round the answer to at least four decimal places. The probability that the sample mean income is between 41 and 44 is . (c) Find the 70th percentile of the sample mean. Round the answer to at least one decimal place. The 70th percentile of the sample mean is . (d) Would it be unusual for the sample mean to be less than 38? Round the answer to at least four decimal places. It (Choose one) unusual because the probability of the sample mean being less than 38 is .
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The mean annual income for people in a certain city (in thousands of dollars) is 40, with a standard deviation of 28. A pollster draws a sample of 90 people to interview. 1) What is the probability that the sample mean income is less than 38? Round the answer to atleast four decimal places. 2) What is the probability that the sample mean income is between 38 and 46? Round the answer to atleast for decimal places 3) Find the 40th percentile of the sample mean. Round the answer to atleast one decimal place. 4) Would it be unusual for the sample mean to be less than 38? Round the answer to atleast four decimal places. 5) Do you think it would be unusual for an individual to have an income of less than 38? Explain. Assume the population is approximately normal. Round the answer to atleast four decimal places.
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