A manufacturer of compact fluorescent light bulbs advertises that the distribution of the lifespans of these light bulbs is approximately normal with a mean of 9,000 hours and a standard deviation of 1,000 hours. Define the random variable X to be the life span of compact Fluorescent light bulbs.

1. What is the probability a randomly selected compact fluorescent light bulb will last more than 12,500 hours?

Probability statement with the random variable:

z-score given to 2 decimal places:

probability given to 4 decimal places:

2. Suppose we randomly select a sample of size 15 compact fluorescent light bulbs. State the mean and standard deviation, with proper units,of lifespan for this sample.Round values to 1 decimal place as needed.

Mean:

Standard Deviation:

3. Can the distribution of the sample mean lifespan of compact fluorescent light bulbs based on samples of size 15 be approximated by a normal distribution?

A. No because the sample is not 30 or more

B. Yes becuase the lifespan of these light bulbs is normal

4. What is the probability the mean lifespan of the 15 light bulbs is more than 9,500 hours.

Probability statement:

z-score given to 2 decimal places:

probability given to 4 decimal places:

5.What is the probability the mean lifespan of the 15 light bulbs is between 8,500 hours and 9,200 hours?

Probability statement:

Smaller z-score rounded to 2 decimal places:

Larger z-score rounded to 2 decimal places:

Probability given to 4 decimal places:

6. 85% of the compact fluorescent bulbs in a sample of size 15 have an average life span of at least how many hours? Round answer to 1 decimal place.

Approximately 35% of a population has blood type O+. Suppose we take a random sample of 7 blood donations from a single day.

Define the random variable B as follows

B: the blood type is O+

1. Show/discuss that the given scenario meets the 4 binomial requirements. Please use complete sentences.

2. State the probability of success to 2 decimal places

3. State the sample size.

4. What is the probability that exactly 2 of the 7 selected donations will be type O+?

Include the probability statement with the random variable and give the numerical value to 3 decimal places.

5. What is the probability that less than 3 of the 7 selected donations will be type O+?

Include the probability statement with the random variable and give the numerical value to 3 decimal places.

6. What is the probability that at least 6 of the 7 selected donations will be type O+?

Include the probability statement with the random variable and give the numerical value to 3 decimal places.

7. How many of the donations do we expect to be type O+?

Give the exact value.

8. Suppose we now take a random sample of 100 blood donations. State the mean and standard deviation for this random sample.

Mean:

Standard Deviation (one decimal place):

9.Can the binomial random variable B, with a sample size of 100, be approximated by a normal distribution? Briefly explain/show why or why not.

10. What is the probability, in the sample of size 100, that less than half of the donations will be type O+?

Give the probability statement with the random variable and your answer to 4 decimal places.

1. Suppose the true population proportion were p = 0.6 and a researcher takes a simple random sample of size n = 50. Define phat (p^) to be distribution of the sample proportion.

State the mean of phat:

State the standard deviation of phat (2 decimal places):

2. Show the verification that the distribution of phat can be approximated by a normal distribution.

3.Calculate the probability that the sample proportion will be larger than 0.65.

Give the probability statement with the random variable and the numerical value to 4 decimal places.

According to creditcard.com, 29% of adults do not own a credit card.

Use this information to answer the next 6 questions.

1. Suppose a random sample of 500 adults is asked, "Do you own a credit card?"

State the mean and standard deviation of the sampling distribution of the sample proportion.

Mean:

Standard Deviation (4 decimal places):

2.Can the distribution of the sample proportion, based on the sample of size 500, be approximated by a normal distribution? Show/explain how the requirements are or are not met.

3. What is the probability that in a random sample of 500 adults, less than 32% do not own a credit card?

State the probability statement with the random variable phat, the z-score, and the answer to 4 decimal places.

Probability Statement:

z-score:

Answer:

4.What is the probability that in a random sample of 500 adults, more than 30% do not own a credit card? State the probability statement with the random variable phat, the z-score, and the answer to 4 decimal places.

Probability Statement:

z-score:

Answer:

5.What is the probability that in a random sample of 500 adults, between 25% and 35% do not own a credit card? State the probability statement with the random variable phat, the z-scores, and the answer to 4 decimal places.

Probability Statement:

smaller z-score:

larger z-score:

Answer:

6. What is the probability, in the random sample of 500 adults, 125 or fewer do not own a credit card? The answer should include the probability statement and the probability to 4 decimal places.