Mean Frequency Distribution AP Stat

Which of the following is the best estimate of the standard deviation of the distribution shown in the figure?

• 5

• 10

• 20

• 30

• 4

The tail length of Siberian tigers is approximately normally distributed with a mean of 0.85 meter and a standard deviation of 0.13 meter.

Which of the following is the best interpretation of the z-score for a particular Siberian tiger with a tail length of 0.8 meter?

• The tiger’s tail length is approximately 0.38 standard deviation below the mean.

• The tiger’s tail length is approximately 0.38 standard deviation above the mean.

• The tiger has an approximate 0.38 probability of having a tail length of 0.8 meter.

• The tiger’s tail length is approximately 0.0065 meter greater than the standard deviation.

• The tiger’s tail length is approximately 0.05 meter below the mean

For a certain population of penguins, the distribution of weight is approximately normal with mean 15.1 kilograms (kg) and standard deviation 2.2 kg Approximately what percent of the penguins from the population have a weight between 13.0 kg and 16.5 kg?

• 17%

• 34%

• 57%

• 68%

• 74%

Zucchini weights are approximately normally distributed with mean 0.8 pound and standard deviation 0.25 pound. Which of the following shaded regions best represents the probability that a randomly selected zucchini will weigh between 0.55 pound and 1.3 pounds?

• 
• 
• 
• 
• 

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?

• 0.17

• 0.25

• 0.36

• 0.83

• 0.95

A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation. Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

• The samples were not selected at random.

• The sample size was not sufficiently large.

• The population distribution was approximately normal.

• The samples were selected without replacement.

• The sample means were less than the population mean.

A bag contains chips of which 27.5 percent are blue. A random sample of 5 chips will be selected one at a time and with replacement. What are the mean and standard deviation of the sampling distribution of the sample proportion of blue chips for samples of size 5 ?

• The mean is 0.275, and the standard deviation is 0.250

• The mean is 0.275, and the standard deviation is 0.156

• The mean is 0.275, and the standard deviation is 0.200.

• The mean is 0.275, and the standard deviation is 0.350

• The mean is 0.275, and the standard deviation is 0.1.00

An online customer service department estimates that about 15 percent of callers have to wait more than 8 minutes to have their calls answered by a person. The department conducted a simulation of 1,000 trials to estimate the probabilities that a certain number of callers out of the next 10 callers will have to wait more than 8 minutes to have their calls answered. The simulation is shown in the following histogram.
Based on the simulation, what is the probability that at most 2 of the next 10 callers will have to wait more than 8 minutes to have their calls answered?

• 0.150

• 0.190

• 0.474

• 0.526

• 0.810

A statistician at a metal manufacturing plant is sampling the thickness of metal plates. If an outlier occurs within a particular sample, the statistician must check the configuration of the machine. The distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. Based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine?

• 19.3 mm

• 20.6 mm

• 22.1 mm

• 23.5 mm

• 24.9 mm