Week 3

25%

A brewery produces cans of beer that are supposed to contain exactly 12 ounces. But owing to the inevitable variation in the filling equipment, the amount of beer in each can is actually a random variable with a normal distribution. It has a mean of 12 ounces and a standard deviation of .30 ounce. About what percentage of their cans of beer will have fewer than 11.8 ounces?

about 50%

A brewery produces cans of beer that are supposed to contain exactly 12 ounces. But owing to the inevitable variation in the filling equipment, the amount of beer in each can is actually a random variable with a normal distribution. It has a mean of 12 ounces and a standard deviation of .30 ounce. If you bought a six-pack of their beer what is the probability that you are going to actually get less than or equal to a total of 72 ounces of beer in your six-pack?

about 50%

A brewery produces cans of beer that are supposed to contain exactly 12 ounces. But owing to the inevitable variation in the filling equipment, the amount of beer in each can is actually a random variable with a normal distribution. It has a mean of 12 ounces and a standard deviation of .30 ounce. If you took a random sample of 100 cans of beer from a production run, what would be the probability that the mean amount would be less than 12 ounces?

flatter and wider

A larger standard deviation of a normal distribution indicates that the distribution becomes:

5%

A supermarket has determined that daily demand for soda has an approximately normal distribution, with a mean of 55 cases and a standard deviation of six cases. For what percentage of days can we expect the number of cases of cola sold to be more than or less than 2 standard deviations from the mean?

<1%

A supermarket has determined that daily demand for soda has an approximately normal distribution, with a mean of 55 cases and a standard deviation of six cases. If the supermarket begins each morning with a stock of 73 cases of cola, for what percentage of days will there be an insufficient number of cases to meet the demand?

Approximately less than 29.50 inches or greater than 34.50 inches

The heights of children 2 years old are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatrician regularly measure the heights of toddlers to determine whether there is a problem. Pediatrician determines that there may be a problem when a child is in the top or bottom of 5% heights. What is the height of a 2 year old that could be a problem

.91

The heights of children 2 years old are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatrician regularly measure the heights of toddlers to determine whether there is a problem. What is the probability such that a 2-year child is shorter than 34 inches.

.65

The heights of children 2 years old are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatrician regularly measure the heights of toddlers to determine whether there is a problem. What is the probability such that a 2-year old is between 30 and 33 inches tall.

8.7%

Suppose a manufacturer of light bulbs produces a 75-watt bulb that burns a mean of 7500 hours before it burns out. It has a standard deviation of 220 hours. What percentage of their bulbs would they have to replace under warranty if they offered a warranty of 7200 hours?

7139

Suppose a manufacturer of light bulbs produces a 75-watt bulb that burns a mean of 7500 hours before it burns out. It has a standard deviation of 220 hours. What warranty should the manufacturer offer (in terms of hours) if they want to replace no more than 5% of the bulbs sold?

.28

X is normally distributed with mean 1,000 and standard deviation 250. What is the probability that X lies between 800 and 1,000?

0.12

X is normally distributed with mean 100 and standard deviation 20. What is the probability that X is greater than 145?

38.8

X is normally distributed with mean 50 and standard deviation 8. What value of X is such that only 8% values are below it? (Hint: In this problem you know the probability and you want to find the value of X - so it goes backward).

exactly .50 ; 1

In a standard normal distribution bell curve, the proportion of the total area which must be to the left of the mean is and the total area under the curve is:

.5

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then the probability of X greater than equal to 75 is: