Question description

 

Unit 4 Lesson 4 Assignment Find the values of the variables (a, b, c etc.) for each problem\

: 1. A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a normal distribution with mean u = 303 ml and standard deviation o = 3 ml.

What is the probability that the sample mean contents of the 10 bottles is less than 300 ml?

P( x <= [a])

z<= [b]

p = [c]

2. A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a normal distribution with mean u = 303 ml and standard deviation o = 3 ml.

What is the probability that the sample mean contents of the 10 bottles is more than 305 ml?

P(x => [a])

z=> [b]

p = [c]

3. For 1998 as a whole, the mean return of all common stocks listed on the New York Stock Exchange (NYSE) was u = 16% and standard deviation o = 26%. Assume that the distribution of returns is roughly normal.

What is the probability a stocks will lose money (u < 0)?

P( x <= [a])

z <= [b]

p = [c]

4. For 1998 as a whole, the mean return of all common stocks listed on the New York Stock Exchange (NYSE) was u = 16% and standard deviation o = 26%. Assume that the distribution of returns is roughly normal.

Suppose we create a portfolio of 8 stocks by randomly selecting stocks from the NYSE and investing equal amounts of money in each stock. What is the sampling distribution for these 8 stocks? N([a], [b])

5. For 1998 as a whole, the mean return of all common stocks listed on the New York Stock Exchange (NYSE) was u = 16% and standard deviation o = 26%. Assume that the distribution of returns is roughly normal.

What is the probability the portfolio loses money on 8 stocks(u < 0)? 

P(x <=0)

z <= [a]

p = [b]

6. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 264 days and standard deviation 16 days. Consider 15 pregnant women from a rural area.

a) What is the mean and standard deviation of these 15 pregnancies?

Mean = [a], Standard Deviation = [b]

b) What is the probability the sample mean length of pregnancy lasts less than 250 days?

z < = [c] p = [d]

c) What is the probability that the sample mean length of pregnancy lasts more than 284 days?

z < = [e] p = [f

7. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 264 days and standard deviation 16 days. Consider 15 pregnant women from a rural area.

What is the probability that the sample mean length of pregnancy lasts between 260 and 275 days for those 15 pregnancies?

P(x <= 260) P(x <= 275)

z <= [a] z <= [c]

p = [b] p = [d]

final p-value = [e]

8. Suppose Y is a random variable representing the true weight of a 16 oz can of coffee. Suppose that the mean of Y is 16.1 oz and that the standard deviation is 1.5. You have a sample of 100 coffee cans.

a) What is the distribution of the sample?

N( [a], [b])

b) What is the probability that the sample weight is less than 15.8 oz?

z <= [c] p = [d

] c) What is the probability that the sample weight is more than 16.4 oz?

z => [e] p = [f]

9. Suppose Y is a random variable representing the true weight of a 16 oz can of coffee. Suppose that the mean of Y is 16.1 oz and that the standard deviation is 1.5. You have a sample of 100 coffee cans.

What is the probability that the sample weight is between 15.7 oz and 16.5 oz for the 100 coffee cans?

P(x <= 15.7) P(x <= 16.5)

z <= [a] z<= [b]

p = [c] p = [d]

p-value = [e]