Math 115-01: Introductory Statistics 8. A set of exam scores is normally distributed with a mean = 72 and a standard deviation = 4. Use Empirical Rule to complete the following sentences. (6 pt.) 68% of the scores are between and 95% of the scores are between and 99.7% of the scores are between and 9. According to a study done by WJU students, the height for Australian adult females is normally distributed with an average of 55 inches and a standard deviation of 1.9 inches. Suppose one Australian adult female is randomly chosen. Let X = height of the individual. Round all answers to 4 decimals places. (6 pts.) a). What is the distribution of X? X~NC b). Find the probability that the person is between 52.1 and 54.7 inches. P = c). The middle 47% of Australian heights lie between what two numbers? Low: inches. High: inches. d). What is the IQR? IQR = 10. In a large population, 63% of the people have been vaccinated. If 6 people are randomly selected, what is the probability that at least one of them has been vaccinated? (1 pt.) Give your answer as a decimal to 4 decimal places. P = 11. A ball is drawn randomly from a jar that contains 5 red balls, 7 blue balls, and 8 yellow balls. Find the probability of a given event and show your answer to 4 decimal places. (5 pts.) a). A red ball is drawn. P(red) = b). A blue ball is drawn. P(blue) = c). A blue or a red ball is drawn. P(blue or red) = d). A blue ball is drawn and then a yellow ball is drawn. P(blue and yellow) = You put the blue ball in your pocket before draw the yellow one.) e). A white ball is drawn. P(white) = 18Math 115-01: Introductory Statistics Wheeling University - Fall 2022 12. A home pregnancy test was given to women, table shoes the home pregnancy test results. (4 pts.) women, then the pregnancy was verified though blood test. The following Pregnant Positive Negative Total Not Pregnant 77 4 81 Total 50 59 86 54 140 Find the following. Give your answers to 4 decimal places. a). P(Positive | Pregnant) = b). What is the probability that the woman is pregnant given that the test is positive? c). Given that a woman is pregnant, what is the probability that the test is negative? d). P(Not Pregnant | Negative) = 15. Increasing the sample size and decreasing the level of confidence are two ways of obtaining a narrower maria of error for a confidence interval. (1 pt.) true false 14. The manager of a computer ret retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.9 years and a standard deviation of 0.95 years. He then randomly selects records on 39 laptops sold in the past. Round the answer for the following questions to 4 decimal places. (7 pts ) a). What is the distribution of X? X~NC b). What is the distribution of X? X~N c). What is the probability that one randomly selected laptop is replaced less than 3.1 years. P = d). For 39 laptops, find the probability that the average replacement time is less than 3.1 years. P = (Answer as yes or no.) e). For part d) is the assumption of normal necessary? /12 Page 5 of 8Wheeling Math 115-01: Introductory Statistics 15. Assume that a sample is used to estimate a population mean u. Find the 90% confidence interval for a sample of size 533 with a mean of 62.7 and a standard deviation of 13.4. Enter your answer as a tri-linear inequality accurate to 3 decimal places. (2 pts.)