Midterm Exam 2

1.  In a genetics experiment on​ peas, one sample of offspring contained 185 green peas and 216 yellow peas. Based on those​ results, estimate the probability of getting an offspring pea that is green.  Express your answer as a percentage rounded to the nearest hundredth without the % sign.

2.  Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. ​

If one order is​ selected, find the probability of getting an order from Restaurant C or an order that is accurate. Express your answer as a percentage rounded to the nearest hundredth without the % sign.

3. Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. ​

If three different orders are​ selected, find the probability that they are all from restaurant B. Assume that the orders are selected without replacement. Express your answer as a percentage rounded to the nearest hundredth without the % sign.

4.  Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. ​

If one order is​ selected, find the probability of getting an accurate order given the order is from Restaurant A. Express your answer as a percentage rounded to the nearest hundredth without the % sign.

5.  A study conducted at a certain college shows that 37% of the school’s graduates find a job in their chosen field within a year after graduation. Find the probability that among 12 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. Assume that the sample is taken with replacement. Express your answer as a percentage rounded to the nearest hundredth without the % sign.

6.  In the town of Maplewood a certain type of DVD player is sold at just two stores. 36% of the sales are from store A and the rest of the sales are from store B. 8% of the DVD players sold at store A are defective while 7% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A? Express your answer as a percentage rounded to the nearest hundredth without the % sign.

7. How many ways can 3 people be chosen and arranged in a straight line if there are 8 people to choose from?

8.  The library is to be given 8 books as a gift. The books will be selected from a list of 20 titles. If each book selected must have a different title, how many possible selections are there?

9  Find the missing value required to create a probability distribution, then find the standard deviation for the given probability distribution. Round to the nearest hundredth.

10,   A contractor is considering a project that promises a profit of $19,040 with a probability of 0.61. The contractor would lose (due to bad weather, strikes, and such) of $3,576 if the project fails. What is the expected profit? Round to the nearest cent.

11.  According to a college survey, 54% of all students work full time. Find the mean for the number of students who work full time in samples of size 181 (rounded to the nearest hundredth).

12. An archer is able to hit the bull’s-eye 46% of the time. If she shoots 11 arrows, what is the probability that she gets exactly 2 bull’s-eyes? Assume each shot is independent of the others. Express your answer as a percentage rounded to the nearest hundredth without the % sign.

13.  A body temperature of 96.46° F given that human body temperatures have a mean of 98.38° F and a standard deviation of 0.85°F. Determine if the value is unusual. Why or why not? Explain your answer using descriptive statistics and/or probability appropriately. If your reasoning requires a z-score, enter the z-score rounded to the nearest hundredth. If your reasoning requires a probability, enter the probability as a decimal rounded to the nearest ten-thousandth.

14.  A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 1.4. Find the probability that on a randomly selected trip, the number of whales seen is 5. Express your answer as a percentage rounded to the nearest hundredth.

15.   Suppose the probability of contracting a certain disease is 1 in 63 for a new case in a given year. Approximate the probability that in a town of 202 people there will be at least one new case of the disease next year. Express your answer as a percentage rounded to the nearest hundredth without the % sign.

16.  Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn’t possible. He said that the expected value was the most likely value in a single roll of the die, and since it wasn’t possible for a die to turn up with a value of 3.5, the expected value couldn’t possibly be 3.5. Who is right?

17. Draw the standard normal distribution. Shade the area between the z-score of 0.84 and 4.52. Find the shaded area. Round to the nearest ten-thousandth.

18. Draw the standard normal distribution. The shaded area to the left of the z-score is 0.0314. Find the z-score. Round to the nearest hundredth.

19.  Suppose that replacement times for washing machines are normally distributed with a mean of 5.9 years and a standard deviation of 3.4 years. Find the replacement time that separates the top 10.2% from the rest. Round to the nearest hundredth.

20.  The weights of the fish in a certain lake are normally distributed with a mean of 5.6 lb and a standard deviation of 1.2 lb. If 11 fish are randomly selected, what is the probability that the mean weight will be between 4.5 and 5.5 lb? Express the answer as a percentage rounded to the nearest hundredth without the % sign.

21.  Approximate the probability that in 63 tosses of a fair die, more than 13 threes will be obtained. Express the probability as a decimal rounded to the nearest thousandth.