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?

- 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.**

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