Question

Probability and Statistics

Could you please solve the following questions with specifying the answers

A. Is the distribution of incomes in the US described by a normal distribution with μ equal to the mean income?

1. Yes    b. No    c. Not enough information

B. The weights of baby orangutans has standard deviation 4 pounds. How large a sample of baby orangutans is necessary for the 95% margin of error to be .5 pounds?

a. 144      b. 324      c. 256   d. 900

C. A car manufacturer says their cars average 26 miles per gallon of gas at 65 miles per hour a standard deviation of σ = 2 miles per gallon.. A Consumer group tested 100 such cars and found the average x̅₁₀₀ to be 25.4 miles per gallon. Is this sufficiently small to reject the null hypothesis H₀: μ = 26 miles per gallon? (No table needed.)

a. Yes     b. No     c. Not enough information.

Answer 1

A) Yes because

Option a ) is correct.

B)

Solution :

Given that,

standard deviation = \sigma = 4

margin of error = E = 0.5

At 95% confidence level the z is ,

\alpha = 1 - 95% = 1 - 0.95 = 0.05

\alpha / 2 = 0.05 / 2 = 0.025

Z\alpha/2 = Z0.025 = 1.960

Sample size = n = ((Z\alpha/2 * \sigma ) / E)2

= ((2 * 4) / 0.5)2

= 256

Sample size = 256

Option b ) is correct.

C)

Test stat

Note we are not given any information about the significance level. So given info is not enough for any conclusion.

Ans ; c . Not enough information.

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