Sampling Distributions Practice

a company is hiring new staff and has a budget of £22000 p.a. with a standard deviation of £2500 (depending on qualifications). If a random sample of 50 applicants is taken, what is the probability that the average starting salary requested is more than £23000?

(You may use a formula sheet and/or statistical tables.)

• 0.0023

• 0.4977

• 0.1554

• 0.3446

Tags

CCSS.HSS.ID.A.4

Businesses in a certain sector must submit safety forms once a month. Inspectors believe it should take on average 33 minutes to complete a form with a standard deviation of 8 minutes. In a survey, a random sample of 40 managers are asked how long it takes them to submit the form. What is the probability that the sample mean time is greater than 35 minutes?

• 0.4429

• 0.0987

• 0.4013

• 0.0571

Tags

CCSS.HSS.ID.A.4

A bakery has, each day, an average of 60 customers with a standard deviation of 12. If 9 days are selected at random, what is the probability that the average number of customers recorded for these 9 days is less than 56?

(You may use a formula sheet and/or statistical tables.)

• 0.1293

• 0.1587

• 0.3707

• 0.3413

Tags

CCSS.HSS.ID.A.4

What is the relationship between the mean of the population and the mean of the sampling distribution of the sample means?

• the mean of the population is greater than the mean of the sampling distribution of the sample means.

• the mean of the population is lesser than the mean of the sampling distribution of the sample means.

• the mean of the population is equal to the mean of the sampling distribution of the sample means.

• the mean of the population is not equal to the mean of the sampling distribution of the sample means.

Tags

CCSS.6.SP.A.2

What is the equivalent value of the standard deviation of the sampling distribution of the sample means in comparison to the standard deviation in an infinite population?

• 
• 

What have you observed with the histogram of the sampling distribution of the sample mean?

• The histogram is skewed to the left, regardless of the shape of the population.

• It will tend to have an abnormal distribution, regardless of the shape of the population.

• The bar in the histogram will be equally distributed

• It will tend to have a normal distribution, regardless of the shape of the population.

According to the Central Limit Theorem, For a sample to be large enough, the sample size should be ______.

• half of the population

• 75% of the population size

• at least 30

• at most 100

Tags

CCSS.HSS.ID.A.4

The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25. 
What is the mean of the sampling distribution?

• 400
• 40
• 25
• 8

The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25. 
What is the standard error of the sampling distribution?

• 400
• 40
• 25
• 8

 A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years.  The ages are normally distributed. What is the probability that a randomly selected student is older than 16.5 years old?

• 0.864
• 0.879
• 0.121
• None of these

Tags

CCSS.HSS.ID.A.4