Question

Probability and Statistics
Could you please solve the following questions with specifying the answers

A. The weights of the boys in a city are normally distributed with μ = 85 pounds and σ = 6. What is the probability three randomly selected boys all weigh 73 pounds or less?

1. 3(.025)        b. 3(.16)        c. (.025)³ d.(.135)³

B. If in a sample of 1600 voters, 56% favor candidate A and the remaining 44% favor B, what is a 95% confidence interval for the percentage favoring candidate A?

a. 56%±5%       b. 56%±2.5%     c. 56%±1.25%     d. 56%±.5%           

C. The manufacturers of a certain kind of tire would like to know how long the tires last. Assume the distribution is normal. A study shows that 144 randomly selected tires last an average of 28,200 miles with a standard deviation of 2,500 miles. What is a 95% confidence interval for the average life of this type of tire?

a.   28,200 ± 301 miles   b. 28,200 ± 319    c. 28,200 ± 417    d. 28,200 ± 612

Answer 1

Ans:

a)73 is 2 standard deviations below the mean.

As,95% of the data falls within 2 standard deviations of the mean.

Probability that weight will be less than 73=(1-0.95)/2=0.025

So,probability that the three randomly selected boys all weigh 73 pounds or less=(0.025)^3

Option c is correct.

b)

Point estimate=0.56

Margin of error=2*SQRT(0.56*(1-0.56)/1600)=0.025

95% confidence intreval is 56%+/-2.5%

Option b is correct.

c)

sample mean=28,200

Margin of error=2*(2500/SQRT(144))=417

95% confidence interval for the average life

=28,200+/-417

Option c is correct.