# Probability and statistics problems?

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.

What is the probability that z, the standard normal distribution, is less than 1.75 standard deviations below the mean of zero?

a. 5% b. 4% c. 6% d. 7.4%

### 2 Answers

- AlanLv 72 months ago
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.)

Z_hat = (x_hat-mean)/ (standard deviation/sqrt(N)) =

Z_hat = (25.4-26)/ (2/sqrt(100) ) = -0.6/(2/10) = -3

so with no table needed

You can use the empirical rule with +/- 3 SDs = 99.7 % so

as long as alpha is greater than 0.003

then it is sufficiently small enough

so unless you are picked an alpha < 0.003 or 3/10 of a percent

P(z< -3) = (1.--0.997)/2 = approx 0.0015

so a. Yes (unless you picked an alpha less than 0.003 )

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

b.

Read from a z-table

https://www.math.arizona.edu/~rsims/ma464/standard...

P(z< -1.75) = .04006

multiply by 100 to turn into a percentage = 4.006 %

so b. 4%

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- J.B.SchneiderLv 72 months ago
The question is defective and must be revised. The quality of gasolines vary. Sometimes exceeding 5% in efficiency.

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