The random variables A and B follow normal distribution. It is know that the random variable A has a standard deviation o1 = 6, and the random variable B has a standard deviation o2 = 5. Take a sample size of 50 from each random variable; we obtain 21 bar (average) =78 and 22 bar(average) = 87. We conclude that the mean of variable A is higher. O True O False

> Question 4 The lengths of adult males' hands are normally distributed with mean 192 mm and standard deviation is 7 mm. Suppose that 7 individuals are randomly chosen. Round all answers to 4 where possible. a. What is the distribution of ? - N( b. For the group of 7, find the probability that the average hand length is more than 188. c. Find the first quartile for the average adult male hand length for this sample size. d. For part b), is the assumption that the distribution is normal necessary? O No Yes Hint: Some Helpful Videos: • Finding the Sampling Distribution [+] • Finding a Probability Using the Central Limit Theorem [+] • Finding Value Given a Probability Using the Central Limit Theorem [+] . The Central Limit Theorem For ns [+] Hint Submit Question 40 % $ R 5 16 T 4- ^ 6 4+ Y 90 & BA 7 * U 19 144 8 ly 1 tio C I DII 9 DDI O P A

Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.   A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs.   College A 3.7 3.2 3.0 2.5 2.7 3.6 2.8 3.4             College B 3.8 3.2 3.0 3.9 3.8 2.5 3.9 2.8 4.0 3.6 2.6 4.0 3.6     Construct a​ 95% confidence interval for μ1−μ2, the difference between the mean GPA of college A students and the mean GPA of college B students. Round to two decimal places. ​(Note: x1=​3.1125, x2=​3.4385, s1=​0.4357 s2=0.5485

We learned that there are 4 items by which we characterize a distribution in statistics. Which of the followings is NOT one of them? O a. Central tendency Ob. Homogeneity O c. Skewness Od. Kurtosis