Midterm 2 Practice Test

1.  In a genetics experiment on​ peas, one sample of offspring contained 110 green peas and 170 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 A or an order that is not 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 with 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.

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

5.A study conducted at a certain college shows that 26% of the school’s graduates find a job in their chosen field within a year after graduation. Find the probability that among 14 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. 21% of the sales are from store A and the rest of the sales are from store B. 2% of the DVD players sold at store A are defective while 5% 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. There are 8 members on a board of directors. If they must elect 2 titled officers, how many different slates of candidates are possible?

8.  There are 14 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible?

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 $34,252 with a probability of 0.68. The contractor would lose (due to bad weather, strikes, and such) of $5,528 if the project fails. What is the expected profit? Round to the nearest cent.

11.  According to a college survey, 55% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 284 (rounded to the nearest hundredth).

12. An archer is able to hit the bull’s-eye 55% of the time. If she shoots 13 arrows, what is the probability that she gets exactly 6 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 survey for brand recognition is done and it is determined that 60% of consumers have heard of Dull Computer Company. A survey of 16 randomly selected consumers is to be conducted. For such groups, would it be significantly high to get 14 consumers who recognize the Dull Computer Company name? 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.  The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.2. Find the probability that in a randomly selected year, the number of lightning strikes is 2. Express your answer as a percentage rounded to the nearest hundredth.

15.   Suppose the probability of contracting a certain disease is 1 in 70 for a new case in a given year. Approximate the probability that in a town of 260 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. A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates there is a 89% probability that the calculator will work on any given day. Because the final exam is so important, she plans to bring in two calculators in case one loses power. Does she gain much by bringing in the backup calculator? Calculate the probability that she will be able to complete her exam with a working calculator. (Express your answer as a percent rounded to the nearest hundredth without the % sign.)

17.  Draw the standard normal distribution. Shade the area between the z-score of 1.99 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 0.3707. 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 2.1 years. Find the replacement time that separates the top 12.1% 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 6.1 lb and a standard deviation of 2.1 lb. If 50 fish are randomly selected, what is the probability that the mean weight will be less than 5.8 lb? Express the answer as a percentage rounded to the nearest hundredth without the % sign.

21.   Approximate the probability that in 71 tosses of a fair die, fewer than 6 fives will be obtained. Express the probability as a decimal rounded to the nearest thousandth.