Sampling Distribution and CLT

30% of all dogs in a city are micro-chipped. In a sample of 500 dogs, what is the probability that less than 32% of dogs are micro-chipped?

• 0.2586

• 0.1587

• 0.8354

• 0.1398

• 0

According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.

Which of the following is true concerning the shape of the sampling distribution?

• The sampling distribution is normal because n > 30

• The sampling distribution is not normal because nq is < 30

• The sampling distribution is normal because 93% of 180 is > 10

• The sampling distribution is normal because np and nq are both > 10

Knowing that the result of flipping a coin is equally likely (that means, 50/50 chance of observing either outcome). If you flip a coin 500 times, approximate the probability that at least 51% of them will be Tails.

• Essentially 0.

• 0.2891

• 0.3274

• 0.8512

• 0.8236

Your mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit.

What is the mean?

• 0.9

• 0.1

• 500

• 450

• 0.5

Your mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit.

What is the standard deviation?

• 0.04

• 0.004

• 0.3

• 0.03

Your mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit.

What Is the probability that more than 95% of the orders are delivered within three working days?

• 0.0228

• 0.4779

• 0.0478

• 0.9522

According to government data, 22% of American children under the age of six live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 400 children.

What is the probability that between 15% and 25% of children live in households with less than the official poverty level?

• 0.9998

• 0.0007

• 0.9259

• 1

• 0

According to government data, 22% of American children under the age of six live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 400 children. What is the probability that at most 16% of children live in households with less than the official poverty level?

• 0.0003

• 0.0019

• 0.9968

• 0.9999

• 0

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  Let p-hat be the proportion of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week. What is the probability that 38.56% or fewer went to church last week?

• 0.9999998

• 0.8929

• 0.1071

• 0.3541

A realtor has been told that 43% of homeowners in a city prefer to have a finished basement. She surveys a group of 300 homeowners randomly chosen from her client list. Describe the sampling distribution model of the proportion of homeowners in this sample who prefer a finished basement.

• mean = 43%; standard deviation = 1.4%

• mean = 57%; standard deviation = 2.9%

• mean = 57%; standard deviation = 1.4%

• mean = 43%; standard deviation = 2.9%

• There is not enough information to describe the distribution.