Question

A study found that highway drivers in one stare traveled at an average speed of 60.8 miles per hour (MPH). Assume the population standard deviation is 6.7 MPH. Complete parts a through d below. a. What is the probability that a sample of 30 of the drivers will have a sample mean less than 59 MPH? P (*<59) - (Round to four decimal places as needed.) b. What is the probability that a sample of 50 of the drivers will have a sample mean less than 59 MPH? P(x<59) - (Round to four decimal places as needed.) c. What is the probability that a sample of 70 of the drivers will have a sample mean less than 59 MPH? P(x<50) - (Round to four decimal places as needed.) d. Explain the difference in these probabilities and the same means the population mean of 60.8 MPH. Therefore, the probability of observing a As the sample size increases the standard error of the mean sample mean less than 50 MPH According to a research Institution, men spent an average of 136 87 on Valentine's Day men who celebrate Valentine's Day was selected. Complete parts a through is in 2009. Assume the standard devon for this population is $45 and that it is normally distrutod. A random sample of 10 a. Calculate the standard error of the mean (Pound to two decimal places as needed.) b. What is the probability that the sample mean will be less than $1257 PG<$125) - (Round to four decimal places as needed.) c. What is the probability that the sample mean will be more than $145? P(x>$145) = (Round to four decimal places as needed.) d. What is the probability that the sample mean will be between $110 and $1607 P ($110 SXS $160) (Round to four decimal places as needed) e. Identify the symmetrical interval that includes 95% of the sample means the true population mean is $136.87 $ sxss (Round to the nearest dollar as needed)