1. (05.01 LC) Sherry is cooking chicken for her family. She wants to be sure the

Question

1. (05.01 LC) Sherry is cooking chicken for her family. She wants to be sure the chicken has an internal temperature of at least 170 degrees Fahrenheit. She uses a thermometer to measure the internal temperature at four randomly chosen places. The minimum reading in the sample is 180 degrees Fahrenheit. Identify the population, the parameter, the sample, and the statistic.

2. (05.01 MC) Fifty-eight percent of the fish in a large pond are minnows. Imagine scooping out a simple random sample of 20 fish from the pond and observing the sample proportion of minnows. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.

3. (05.02 LC) A population has = 75 and a standard deviation of = 10.2. What are the mean and standard deviation of the sampling distribution x if a sample of 400 were taken?

4. (05.02 MC) The amount of icing on a Cuppie Cake large cupcake follows a Normal distribution, with a mean of 2 ounces and a standard deviation of 0.3 ounce. A random sample of 16 cupcakes is selected every day and measured. What is the probability the mean weight will exceed 2.1 ounces?

5. (05.02 MC) The average ACT score follows a Normal distribution, with a mean of = 21.1 and a standard deviation of = 5.1. What is the probability that the mean IQ score of 50 randomly selected people will be more than 23?

6. (05.01 HC) Monogram Masters states on its website that 92% of its orders are ready to ship within five working days. A simple random sample of 200 of the 3,000 orders received during the past month are pulled for an audit. The audit shows that 175 of these orders were shipped on time. Part A: If Monogram Masters really ships 92% of its orders within five working days, what is the probability that the proportion in the simple random sample of 200 orders is as small as the proportion in the auditors' sample or smaller? (5 points) Part B: A customer says, "Monogram Masters claims 92% of its orders are shipped on time, but its sample proportion is less than that." Explain why the probability calculation shows the result of the sample agrees with the 92% claim. (5 points) (10 points)

7. (05.02 MC) Carson's tablet has about 2,000 videos. The distribution of the play times for these videos is skewed heavily to the right, with a mean of 135 seconds and a standard deviation of 25 seconds. Part A: Explain why you cannot accurately calculate the probability that the mean play time is more than 142 seconds for a random sample of 10 videos. (4 points) Part B: Suppose you take a random sample of 50 videos instead. Explain how the Central Limit Theorem allows you to find the probability that the mean play time is more than 142 seconds. Calculate this probability. Show your work. (6 points) (10 points)

Explanation / Answer

2)
p = 0.58 , n =20

Std.dev. = sqrt( p * ( 1 - p) / n)
= sqrt ( 0.58 * (1 - 0.58) / 20)
= 0.11036

3)
mean = 75 , s = 10.2 , n = 400

mean = 75 , std.dev. = s / sqrt(n)
= 10.2/sqrt(400) = 0.51

4)

mean = 2 , s = 0.3 , n =16

P(x > 2.1)
z = ( x - mean) / ( s/sqrt(n))
= ( 2.1 - 2) / ( 0.3/sqrt(16))
= 1.333

P(X > 2.1) = P(z > 1.333) = 0.0912 by standard normal table

5)
mean = 21.1 , s = 5.1 , n =50
p(x > 23)
z = ( x - mean) / ( s/sqrt(n))
= ( 23 - 21.1) / ( 5.1/sqrt(50))
= 2.6343

P(X > 23) = P(z > 2.63423) = 0.0042 by standard normal table

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