Exam 9: Sampling Distributions

Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean between 395.5 and 404.5 is ___.

Suppose a population has a mean of 870 and a variance of 1,600. If a random sample of size 64 is drawn from the population, the probability that the sample mean is between 860 and 875 is ___.

Suppose 40% of the population of pre-teens have a TV in their bedroom. If a random sample of 500 pre-teens is drawn from the population, then the probability that 44% or more of the pre-teens have a TV in their bedroom is ___.

Certain transportation company has a fleet of 210 vehicles. The average age of the vehicles is 4.25 years, with a standard deviation of 18 months. In a random sample of 40 vehicles, what is the probability that the average age of vehicles in the sample will be less than 4 years?

Suppose the population of all colleges shows the annual parking fee per student is $110 with a standard deviation of $18. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean of more than $115 is ___.

According to the central limit theorem, if a sample of size 56 is drawn from a population with a standard deviation of 14, the standard deviation of the distribution of the sample means would equal ___.

Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean less than 15 minutes is ___.

Suppose 40% of all college students have a computer at home and a sample of 64 is taken. What is the probability that more than 30 of those in the sample have a computer at home?

If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is more than 0.89?

Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean of more than 404.5 is ___.

The sampling distribution of the sample means is less variable than the population distribution.

It is known that 30% of XYZ Corporation's 25,000 employees are millionaires. If a random sample of 100 XYZ's employees is selected, what proportion of the sample will have more than 36% millionaires?

The sampling distribution of the sample means is close to the normal distribution only if the distribution of the population is close to normal.

A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods. Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. If the population of rods has a mean length of 120 cm and a standard deviation of 0.05 cm, the probability that Claude's sample has a mean between 119.985 and 120.0125 cm is ___.

Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean less than 14 minutes is ___.

A population has a mean age of 45 years with a standard deviation of 3 years. If a random sample of 64 is drawn from this population, what is the probability that the sample mean is greater than 45.3 years?

Suppose the population of all colleges shows the annual parking fee per student is $110 with a standard deviation of $18. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a sample mean between $100 and $115 is ___.

The sampling distribution of has a mean equal to the square root of the population proportion π.

The standard deviation of a sampling distribution of the sample means is commonly called the standard error of the mean.

A correction for continuity must be made when approximating the binomial distribution problems using a normal distribution.