1.A population of values has a normal distribution with

=

184.6

=184.6

and

=

49.3

=49.3

. You intend to draw a random sample of sizen

=

241

n=241

.

1. Find the probability that a single randomly selected value is greater than 183.6.
2. P(X> 183.6) =Round to 4 decimal places.
4. Find the probability that the sample mean is greater than 183.6.
5. P(
6. X
7. X
8. > 183.6) =Round to 4 decimal places.

Answers obtained using exactz-scores orz-scores rounded to 2 decimal places are accepted.

2.A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 171 lb and a standard deviation or 34 lb. You need to design an elevator that will safely carry 13 people. Assuming a worst case scenario of 13 male passengers, find the maximum total allowable weight if we want a 0.999 probability that this maximum will not be exceeded when 13 males are randomly selected.

maximum weight =-lb Round to the nearest pound.

Answers obtained using exactz-scores orz-scores rounded to 2 decimal places are accepted.

3.A manufacturer knows that their items have a normally distributed length, with a mean of 6.4 inches, and standard deviation of 1.2 inches.

If 23 items are chosen at random, what is the probability that their mean length is less than 5.7 inches?

4.If n=600 and

p

p^

(p-hat) =0.64, find the margin of error at a 99% confidence level

Give your answer to three decimals

5.You measure 41 dogs' weights, and find they have a mean weight of 70 ounces. Assume the population standard deviation is 10.8 ounces. Based on this, what is the maximal margin of error associated with a 95% confidence interval for the true population mean dog weight.

Give your answer as a decimal, to two places

6.You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately

=

63.9

=63.9

. You would like to be 95% confident that your estimate is within 3 of the true population mean.How large of a sample size is required?

[Do not round mid-calculation. However,use a critical value rounded to three decimal places this is important for the system to check answers correctly.]

n=

7.For this problem, use the n=1/m

2

m2

formula.

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 95% confident that your estimate is within 2.6% of the true population proportion. How large of a sample size is required?

n=

4.