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Normal DistributionfCentral Limit Theorem (GW 9) 1. State the 3 important parts of the Central Limit Theorem for the sample mean. 2. The completion time (in minutes) for a student to complete a short quiz follows the continuous probability density function shown here, with some areas calculated. It is known that u:5.3 minutes and o = 2.4 minutes. 40 students take the quiz. a. Find the probability that the mean completion time for the students is under 5 minutes. b. Find the probability that the mean time for the class to nish the quiz is between 5 and 6 minutes. c. The mean completion time for the class was 7.1 minutes. Is this result unusual? Explain. 3. For women aged 18-24, systolic blood pressures (in mmHg) are normally distributed with p=l 14.8 and o=l3.l. a. Find the probability a woman aged 1824 has systolic blood pressure exceeding 120. b. If 40 women are randomly selected, find the probability that their mean blood pressure exceeds 120. c. If the pdf for systolic blood pressure did NOT follow a normal distribution, would your answer to part b change? 4. It has been reported that 28% of all Californians have visited Yosemite National Park. A pollster samples 1000 Californians and determines that 240 of them have visited Yosemite National Park. a. Determine the value of the sample proportion,, of Californians who have visited Yosemite. Is the higher or lower than the reported population value? b. Determine the expected value of the sample proportion. c. Determine the standard deviation of the sample proportion. d. Determine that the condition for normality is satised. e. Determine the probability the sample proportion exceeds 0.24. f. Determine the probability the sample proportion is between 0.2 and 0.3. a\": E I; W Dashboard Calendar To Do Notifications lnbox