1.A couple plans to have five children. Assuming that it is equally likely to have a girl as a boy, what is the probability that the couple have three girls out of the five children?

Round your answer to the ten-thousandths place.

2. Citing recent evidence that HIV infections are best managed when treated early, an influential panel of medical experts has finalized its recommendation that all people ages 15 to 65 be screened for the virus that causes AIDS.

The recommendation from the U.S. Preventive Services Task Force seeks to address one of the key challenges in the fight against HIV/AIDS: The window during which patients respond best to treatment is also the time when symptoms of the disease are least noticeable.

Let us say that an HIV test correctly returns a positive result (person has HIV) 96% of the time.

If forty people with HIV are given this test, what is the expected number of positive results?

Write out the exact answer you get, don’t round.

3. Citing recent evidence that HIV infections are best managed when treated early, an influential panel of medical experts has finalized its recommendation that all people ages 15 to 65 be screened for the virus that causes AIDS.

The recommendation from the U.S. Preventive Services Task Force seeks to address one of the key challenges in the fight against HIV/AIDS: The window during which patients respond best to treatment is also the time when symptoms of the disease are least noticeable.

Let us say that an HIV test correctly returns a positive result (person has HIV) 96% of the time.

If forty people with HIV are given this test, what is the standard deviation number of positive results?

Round to the nearest hundredths place.

4. Citing recent evidence that HIV infections are best managed when treated early, an influential panel of medical experts has finalized its recommendation that all people ages 15 to 65 be screened for the virus that causes AIDS.

The recommendation from the U.S. Preventive Services Task Force seeks to address one of the key challenges in the fight against HIV/AIDS: The window during which patients respond best to treatment is also the time when symptoms of the disease are least noticeable.

Let us say that an HIV test correctly returns a positive result (person has HIV) 96% of the time.

If forty people with HIV are given this test, what is the probability of seeing 35 results or less come back positive?

Round your answer to the ten-thousandths place.

5. You toss a fair die (six-sided) 42 times. What is the probability that a five appears 8 times or more out of the 42 throws?

Round your answer to the ten-thousandths place.

6. A garden shop sells top soil that is sold by the cubic yard.  When a customer buys a cubic yard a front loader is used to scoop the top soil from the storage bin and transfer it to the customers truck; thus the amount transferred to the truck is an approximation. On average the weight of the top soil transferred to a truck is 2,150 lbs. with a standard deviation of 19 lbs.  The weight is normally distributed.

What is the probability that a customer receives over 2200 lbs. of top soil?

Round your answer to the ten-thousandths place.

7. A garden shop sells top soil that is sold by the cubic yard.  When a customer buys a cubic yard a front loader is used to scoop the top soil from the storage bin and transfer it to the customers truck; thus the amount transferred to the truck is an approximation. On average the weight of the top soil transferred to a truck is 2,150 lbs. with a standard deviation of 19 lbs.  The weight is normally distributed.

In a single day, top soil is sold to eight customers. What is the probability that the average weight sold is less than 2,130 lbs.?

Round your answer to the ten-thousandths place.

8. The average pH level of the water in a Lake is 6.11 with a standard deviation of 0.53. Consider the pH distribution of averages from samples of size 20 from the lake. What is the standard deviation for the sampling distribution created from averages of 20?

Round to the nearest hundredths place.