Question

1. A population of N=1200 has a standard deviation of 20. In each of the following cases, which formula will you use to calculate the standard deviation of the sample mean and then use the appropriate formula to calculate it:
a. n=96
b. n=30

2. Dartmouth Distribition Warehouse makes deliveries of a large number of products to its customers. It is known that 85% of all the orders it receives from its customers are delivered on time. Let p-hat be the proportion of orders in a random sample of 100 that are delivered on time. Find the probability that the values of p-hat will be:

a. Less than 80.

3. The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6.0 ounces. Suppose the weight of pucks produced by a factory are normally distributed with a mean of 5.75 oz and a standard deviation of 0.11 oz. What percentage of the pucks produced at this factory cannot be used by the NHL?

4. A yogurt cup is advertised as containing 6 oz of yogurt but the machine that fills the cups doesn't put exactly 6 oz of yogurt into each cup. The amount varies slightly. The amount of yogurt follows a normal distribution with a mean that can be set to any desired amount by adjusting the machine. The standard deviation of the amount of the yogurt is always 0.05 oz, regardless of the mean amount. If the company wants to be at 99% of cups contain at least 6 oz of yogurt, to what level should he set the mean?

5. Seventy percent of adults favor some kind of government control on the prices of medicines. Assume that this percentage is true for the current population of all adults. Let p-hat be the proportion of adults who favor this control in a random sample of 400 adults. Calculate the mean and standard deviation of the sampling distribution and describe the shape of its sampling distribition.

6. The time that it takes students to get to a University from their home has a distribition that is skewed to the right with a mean of 30 minutes and a standard deviation of 20 minutes.

a. Find the probability that the mean time it takes to get from home to a University for a random sample of 60 students is more than 35 minutes.

a. What is the shape of the sampling distribution if a random sample of a random sample of 15 students was selected instead of 60. Can you determine the mean and standard deviation of this new sampling distribition? If so, what are they? If not, why not?

Answer 1

1. Standard deviation of sample mean = population standard deviation/ sqrt(n)

A) standard deviation of sample mean = 20/sqrt(96) = 20/9.79 = 2.04

B) standard deviation of sample mean = 20/ sqrt(30) = 20/5.47 = 3.65

2. P(phat<0.8)  = P( Z < (0.8-0.85) / sqrt(0.85×0.15/100)

= P( Z < - 0.05/ 0.0357)

= P( Z < -1.33)

= 0.0918

Answer 2

The answer to 2 is 0.0918