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Show your PhStat output or manual calculations.Z is less than 1.57Z is between 1.57 and 1.84

1. Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), what is the probability that:

1. Z is greater than 1.84
2.  
3. Z is less than 1.57 or greater than 1.84

 

 

2. Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), what is the probability that:

 

1. Z is between -1.57 and 1.84
2. Z is less than -1.57 or greater than 1.84
3. What is the value of Z if only 25 percent of all possible Z values are larger
4. Between what two values of Z (symmetrically distributed around the mean) will 68.26 percent of all possible Z values be contained?

 

3. Given a normal distribution with m = 100 and s = 10, what is the probability that:

 

1. X > 80?
2. X < 65?
3. X < 75 or X > 90?
4. Between what two X values (symmetrically distributed around the mean) are ninety percent of the values?

 

4. Given a normal distribution with m = 50 and s = 4, what is the probability that:

 

1. X > 45?
2. X < 43?
3. Six percent of the values are less than what X value?
4. Between what two X values (symmetrically distributed around the mean) are sixty-five percent of the values?

 

 

5. In 2014, the per capital consumption of bottled water in the United States was reported to be 34 gallons. Assume that the per capital consumption of bottled water in the United States is approximately normally distributed with a mean of 34 gallons and a standard deviation of 8 gallons.

 

1. What is the probability that someone in the United States consumed more than 32 gallons of bottled water in 2014?
2. What is the probability that someone in the United States consumed between 10 and 18 gallons of bottled water in 2014?
3. What is the probability that someone in the United States consumed less than 8 gallons of bottled water in 2014?
4. Ninety percent of the people in the United States consumed less than how many gallons of bottled water.

 

 

6.

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

a. What is the distribution for the weights of one 25-pound lifting weight? What is the mean and standard deviation?

b. What is the distribution for the mean weight of 100 25-pound lifting weights?

c. Find the probability that the mean actual weight for the 100 weights is less than 24.9.

 

 

7.

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

Draw the graph from Exercise 7.1.

 

 

8.

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

Find the probability that the mean actual weight for the 100 weights is greater than 25.2.

 

 

9.

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

Draw the graph from Exercise 7.3.

 

 

10.

A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.

Find the 90^th percentile for the mean weight for the 100 weights.