 # . If the weight (in grams) of cereal in a box of Lucky Charms is N(484,6),

| November 18, 2015

1.    If the weight (in grams) of cereal in a box of Lucky Charms is N(484,6), what is the probability that the box will contain less than the advertised weight of 460 gm? Note: You may need to use Excel to calculate the exact probabilities.

2.The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 7.0 ml. The mean is adjustable.

(a)

Where should the mean be set to ensure a 95 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)

Mean  =     ml

(b)

Where should the mean be set to ensure a 99 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)

Mean=     ml

(c)

Where should the mean be set to ensure a 99.9 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)

Mean=     ml

3.Jim’s systolic blood pressure is a random variable with a mean of 139 mmHg and a standard deviation of 25 mmHg. For Jim’s age group, 140 is the threshold for high blood pressure.

Assume the data given follows the normal probability distribution.

(a)

If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 130 or less? (Round the value of z to 2 decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimals.)

Probability

(b)

If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 169 or more? (Round the value of z to 2 decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimals.)

Probability

(c)

If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be between 110 and 159? (Round the value of z to 2 decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimals.)

Probability

4. Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.21 claim per month.

(a)

What is the probability that the dealership will wait at least 10 months until the next claim? (Round your answer to 4 decimal places.)

Probability

(b)

What is the probability that the dealership will wait at least a year? (Round your answer to 4 decimal places.)

Probability

(c)

What is the probability that the dealership will wait at least 2 year? (Round your answer to 4 decimal places.)

Probability

(d)

What is the probability that the dealership will wait at least 10 months but not more than 1 year? (Round your answer to 4 decimal places.)

Probability

5. Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 28 minutes and a standard deviation of 2 minutes, while method B has a mean of 32 minutes and a standard deviation of 1.0 minutes.

(a)

Which procedure is preferred if the procedure must be completed within 30 minutes?

Method A

Method B

Either

(b)

Which procedure is preferred if the procedure must be completed within 34.0 minutes?

Either

Method A

Method B

(c)

Which procedure is preferred if the procedure must be completed within 31 minutes?

Method B

Either

Method A

6. Shower temperature at the Oxnard Health Club showers is regulated automatically.The heater kicks in when the temperature falls to 97ºF and shuts off when the temperature reaches 107ºF. Water temperature then falls slowly until the heater kicks in again. At a given moment, the water temperature is a uniformly distributed random variable U(97,107).

Find the 75th percentile for water temperature. (Round your answer to 2 decimal places.)

75th percentile

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