Question 1

Suppose a random sample of n = 64 measurements is selected from a population with mean μ = 65 and and σ. standard deviation $$\sigma = 12 . \text { Find the values of } \mu _ { x } ^ { - } \text {and } \sigma _ { x }^ { - } $$

Accepted Answer

The answer of Suppose a random sample of n =...

Question 2

The weight of corn chips dispensed into a 15-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 15.5 ounces and a standard deviation of 0.1 ounce. Suppose 400 bags of chips are randomly selected. Find the probability that the mean weight of these 400 bags exceeds 15.6 ounces.

Accepted Answer

The answer of The weight of corn chips dispensed into...

Question 3

The average score of all golfers for a particular course has a mean of 73 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 74.

Accepted Answer

The z-score for an average score of 74 is (74 - 73) / 3.5 = 0.29. The probability that the average score of the 49 golfers exceeded 74 is the area under the normal distribution curve to the right of z = 0.29, which is 0.3707.

Question 4

One year, the distribution of salaries for professional sports players had mean $1.8 million and standard deviation $0.6 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players that year exceeded $1.1 million.

Accepted Answer

The sample mean's distribution will be approximately normal due to the Central Limit Theorem. The standard error is 0.6 million / sqrt(400) = 0.03 million. The z-score for 1.1 million is (1.1 - 1.8) / 0.03 = -23.33, which is extremely low, indicating a probability close to 1 that the sample mean exceeds 1.1 million.

Question 5

Suppose a random sample of n = 64 measurements is selected from a population with mean μ = 65 and standard deviation $\sigma = 12 \text {. Find the } z \text {-score corresponding to a value of } \bar { x } = 68 \text {. }$ 3 Find Probability

Accepted Answer

The answer of Suppose a random sample of n =...

Question 6

Suppose a random sample of n = 64 measurements is selected from a population with mean μ = 65 and standard deviation $$\sigma = 12 \text {. Find the probability that } \bar { x } \text { falls between } 65.75 \text { an } 68.75 \text {. }$$

Accepted Answer

The answer of Suppose a random sample of n =...

Question 7

The weight of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of .2 ounce. Suppose 100 bags of chips are randomly selected. Find the probability that the mean weight of these 100 bags exceeds 10.45 ounces.

Accepted Answer

The answer of The weight of corn chips dispensed into...

Quiz 6: Sampling Distributions

Suppose a random sample of n = 64 measurements is selected from a population with mean μ = 65 and and σ. standard deviation $\sigma = 12 . \text { Find the values of } \mu _ { x } ^ { - } \text {and } \sigma _ { x }^ { - }$

The average score of all golfers for a particular course has a mean of 73 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 74.

One year, the distribution of salaries for professional sports players had mean $1.8 million and standard deviation $0.6 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players that year exceeded $1.1 million.

Suppose a random sample of n = 64 measurements is selected from a population with mean μ = 65 and standard deviation $\sigma = 12 \text {. Find the } z \text {-score corresponding to a value of } \bar { x } = 68 \text {. }$ 3 Find Probability

Suppose a random sample of n = 64 measurements is selected from a population with mean μ = 65 and standard deviation $\sigma = 12 \text {. Find the probability that } \bar { x } \text { falls between } 65.75 \text { an } 68.75 \text {. }$