MATH 202 Week 3 Recitation Questions 1) When a production process is operating c
ID: 3209721 • Letter: M
Question
MATH 202 Week 3 Recitation Questions 1) When a production process is operating correctly, the number of units produced per hour has a normal distribution with a mean of 92 and standard deviation of 3.6. dom sample of 4 hours was take a. Find the mean of the sampling distribution of the sample means. b. Find the variance of the sampling distribution of the sample means. c. Find the standard deviations of the sampling distribution of the sample A ran n. means. d. What is the probability the sample mean exceeds 93 units? 2) In 1992, Canadians voted in a referendum on a new constitution. In the province of Quebec, 42.4% of those who voted were in favor of the new constitution. A random sample of 100 voters from the province was taken. a. What is the mean of the distribution of the sample proportion in favor of a new constitution? b. What is the variance of the sample proportion? c. What is the standard error of the sample proportion? d. What is the probability that the sample proportion is more than 0.5? 3) In a large city it was found that summer electricity bills for single-family homes followed a normal distribution with a standard deviation of $100. A random sample of 25 bills was taken. Find the probability that the sample standard deviation is less than $75. Find the probability that the sample standard deviation is more than $150 a. b.Explanation / Answer
ANSWER:
a) the mean of the sampling distribution of the sample mean = 92
b)Variance of the sampling distribution of the sample means = (sd)^2/n = (3.6)^2/4 = 3.24
c) Standard deviation of the sampling distribution of the sample means = sd/sqrt(n) = 3.6/sqrt(4) = 1.8
d) P(X > 93) = P((X - mean)/(sd/sqrt(n)) > (93 - mean)/(sd/sqrt(n)))
= P(Z > (93 - 92)/(3.6/sqrt(4)))
= P(Z > 0.56)
= 1 - P(Z < 0.56)
= 1 - 0.7123
= 0.2877
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.