2 For samples of the specified size from the population described, find the mean

Question

2 For samples of the specified size from the population described, find the mean and standard deviation of the sample mean x. 32) The National Weather Service keeps records of snowfall in mountain ranges. Records ain range, the annual snowfall has a mean of 82 inches anda standard deviation of 16 inches. Suppose the snowfalls are sampled during randomly picked years. For samples of size 64, determine the mean and standard deviation of x. .3 Solve the problem. 33) In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. If 50 different homes are randomly selected, find the probability that their mean energy consumption level for September is greater than 1075 kWh. A) 0.0438 B) 0.2090 C) 0.4562 D) 0.2910

Explanation / Answer

Question 7.2

We are given

Population Mean = µ = 82

Population SD = = 16

Sample size = n = 64

Point estimate for mean for Xbar = µXbar = µ = 82

Point estimate for SD for Xbar = xbar = /sqrt(n) = 16/sqrt(64) = 16/8 = 2

So, correct answer is B.

Question 7.3

We are given that energy consumption levels are normally distributed with

Mean = µ = 1050

SD = = 218

We are given

Sample size = n = 50

We have to find P(Xbar > 1075)

P(Xbar > 1075) = 1 – P(Xbar < 1075)

Z = (Xbar - µ) / [/sqrt(n)]

Z = (1075 – 1050) / [ 218/sqrt(50)]

Z = 25/ 30.82986

Z = 0.810902

P(Z< 0.810902) = P(Xbar<1075) = 0.791289 (by using z-table or excel)

P(Xbar > 1075) = 1 – P(Xbar < 1075)

P(Xbar > 1075) = 1 – 0.791289

P(Xbar > 1075) = 0.208711

Required probability = 0.208711

Correct answer is B.

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