What is the probability that a randomly selected vitamin will contain between 82 and 100 grams of pyridoxine?

CHAPTER 6

 

1. True or false questions.

 

1. The probability that a standard normal random variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between – 2.10 and – 1.50.
2. The probability that a standard normal random variable, Z, is less than 50 is approximately 0.
3. Theoretically, the mean, median, and the mode are all equal for a normal distribution.
4. Any set of normally distributed data can be transformed to its standardized form.
5. The “middle spread,” that is the middle 50% of the normal distribution, is equal to one standard deviation.

 

1. Multiple choice questions.

 

1. In its standardized form, the normal distribution

1. has a mean of 0 and a standard deviation of 1.
2. has a mean of 1 and a variance of 0.
3. has an area equal to 0.5.
4. cannot be used to approximate discrete probability distributions.

1. Which of the following about the normal distribution is not true?

1. Theoretically, the mean, median, and mode are the same.
2. About 2/3 of the observations fall within 1 standard deviation from the mean.
3. It is a discrete probability distribution.
4. Its parameters are the mean, , and standard deviation, .

1. If a particular batch of data is approximately normally distributed, we would find that approximately

1. 2 of every 3 observations would fall between 1 standard deviation around the mean.
2. 4 of every 5 observations would fall between 28 standard deviations around the mean.
3. 19 of every 20 observations would fall between 2 standard deviations around the mean.
4. b and c are correct.

 

• Solve the following problems in separate sheets of paper.

 

1. The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with  = 110 grams and  = 25 grams.

(1) What is the probability that a randomly selected vitamin will contain between 100 and 110 grams of pyridoxine?

(2) What is the probability that a randomly selected vitamin will contain between 82 and 100 grams of pyridoxine?

(3) What is the probability that a randomly selected vitamin will contain at least 100 grams of pyridoxine?

(4)What is the probability that a randomly selected vitamin will contain between 100 and 120 grams of pyridoxine?

(5)What is the probability that a randomly selected vitamin will contain less than 100 grams of pyridoxine?

(6)What is the probability that a randomly selected vitamin will contain less than 100 grams or more than 120 grams of pyridoxine?

(7)Approximately 83% of the vitamins will have at least how many grams of pyridoxine?

 

 

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.

(1) What is the probability that Z is less than 1.15?

(2)What is the probability that Z is more than 0.77?

(3) What is the probability that Z is less than -2.20?

(4)What is the probability that Z is more than -0.98?

(5)What is the probability that Z is between -2.33 and 2.33?

(6) What is the probability that Z is between -2.89 and -1.03?

 

 

1. The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes.

(1) What is the probability that a product is assembled in less than 12 minutes?

(2) What is the probability that a product is assembled in between 14 and 16 minutes?

(3) What is the probability that a product is assembled in between 10 and 12 minutes?

(4) What is the probability that a product is assembled in between 16 and 21 minutes?

(5) What is the probability that a product is assembled in more than 11 minutes?

(7) 15% of the products require more than __________ minutes for assembly.

(8) 90% of the products require more than __________ minutes for assembly.