Practice Problems for Exam 2

1) In a 1 pound bag of skittles the possible colors were red, green, yellow, orange, and

purple. The probability of drawing a particular color from that bag is given below.

(You must show your work to get credit)

Color / Probability
Red / 0.1764
Green / 0.2109
Orange / ?
Yellow / 0.1045
Purple / 0.3055
  1. (1 pt) What is the probability of selecting an Orange skittle?
  1. (1 pt) What is the probability of not selecting a Yellow skittle?
  1. (1 pt) What is the probability of selecting a Red or Green skittle?
  1. (1 pt) What is the probability of selecting a Blue skittle?
  1. (1 pt) What skittle color is the most likely?
  1. (1 pt) Give the expected value the skittle color using the discrete probability distribution above.

2) A study was recently done that emphasized the problem we all face with drinking

and driving. Four hundred accidents that occurred on a Saturday night were

analyzed. Two items noted were the number of vehicles involved and whether

alcohol played a role in the accident. The numbers are shown below:

Frequencies: / Number of Vehicles Involved
Did alcohol play a role? / 1 / 2 / 3
Yes / 51 / 98 / 21
No / 30 / 175 / 25

Suppose we Randomly select 1 accident from the table above:

(You must show your work to get credit)

  1. (6pt) Complete the probability table:

Probabilities: / Number of Vehicles Involved
Did alcohol play a role? / 1 / 2 / 3
Yes
No
  1. (1 pt) What is the probability that alcohol played a role and 2 cars were involved?
  1. (1 pt) What is the probability that 1 car was involved?
  1. (1 pt) What is the probability that alcohol didn’t play a role?
  1. (1 pt) What is the probability that alcohol didn’t play a role or three cars were involved?
  1. (1 pt) What is the probability that at most 2 cars were involved?
  1. (1 pt) Given that alcohol played a role, what is the probability that 1 car was involved?

3) You have 27 songs on your MP3 player and randomly select one to play. One song

is your favorite.

Give the probability of the indicated event:

(You must show your work to get credit)

  1. (1 pt) What is the chance that your favorite song will be the one to play?
  1. (2 pts) When it finishes, you again randomly select a song to play, and it’s the same one! What is the chance of this happening (2 in a row)?
  1. (2 pts) When it finishes, you again randomly select a song to play, and it’s the same one! What is the chance of this happening (3 in a row)?

4) Based on data from a survey of college campuses, 46% of studentsdrinkenergy

drinks. 5 college students are selected randomly. (You must show your work to

get credit)

  1. (1 pt) What is "success"?
  1. (1 pt) What is n?
  1. (1 pt) What is p?
  1. (1 pt) What is q?
  1. (7 pts) The probability distribution is (remember P(x) = nCxpx(q)n-x):

0 / 1 / 2 / 3 / 4 / 5 / 6
  1. (1 pt) Give the mean of this binomial distribution:
  1. (1 pt) Give the standard deviation of this binomial distribution: (use )
  1. (1 pt) Compute the z-score for the outcome x=0 people who say they do not drink energy drinks:

5) In acourt case, a jury pool of 100 people was randomly selected from population in

which51% of the citizens were females.

(You must show your work to get credit)

  1. (1 pt) What is n?
  1. (1 pt) What is p?
  1. (1 pt) What is the expected proportion of females in the jury pool (the mean)?
  1. (1 pt) What is the standard error of the proportion of females in the jury pool? (use
  1. (1 pt) What is the probability that a jury pool of 100 people will have exactly 20females? (remember P(x) = nCxpx(q)n-x)
  1. (1 pt) What is the probability that a jury pool of 100 people will be have 10 or fewerfemales? (Hint: can this binomial be approximated using the normal distribution?)
  1. (1 pt) What is the probability that none of the people in the jury pool are females?
  1. (1 pt) What is the probability that a jury pool of 100 people will have between 15 and 30 females?

6) The height of female Martians are normally distributed with a mean

height of 26.5 inches and a standard deviation of 1.4 inches, while Martian males

have a mean height of 24.4 inches and a standard deviation of 1.2 inches.

(You must show your work to get credit)

  1. (2 pts) Martian buildings typically have doors that are 28 inches high. What percent of Martian females are taller than that?
  1. (2 pts) What percent of Martian males are shorter than 28 inches?
  1. (2 pts) If Martian doors were changed so that 95% of females would be shorter that the height of the doors, what would the new height of Martian doors?
  1. (2 pts) Martina is in the 95th percentile for females. Is she shorter than the 28-inch height of the standard door?
  1. (2 pts) The MartianSpace Force requires that their pilots be between 25 and 27.5 inches tall in order to operate theirspacecraft. What percent of females are within those limits?
  1. (2 pts) If the Martian Space Force redesigned its craft to fit the middle 95% of females, what would the cutoff heights be?

7) A brewery has a filling machine that fills 12 ounce bottles of beer. The amount of

beer poured by this filling machine follows a normal distribution with a mean of 12

ounces and a standard deviation of 0.04 ounce. Quality control sets upper and lower

limits on the acceptable variation in the amount poured. If there are too many high or

low values, the range of acceptable weights can be modified.

(You must show your work to get credit)

  1. (1 pt) If the machine is set to allow fillings between 11.95 g and 12.05 g, what percent of fillings are being rejected?
  1. (1 pt) Is this percentage too high? Explain.
  1. (1 pt) If you wanted to reject only 3% of the fillings, what would you set as your upper and lower limits on the machine?

8) The weight of a mature cardinal is normally distributed with a mean of 78 grams and

a standard deviation of 7.4 grams. 90% of all Cardinals are between what two

weights?

(You must show your work to get credit)

  1. (2 pts) 10% ofcardinals die because their weight is below a minimum. What value is this minimum?
  1. (2 pts) 5% of cardinals die because their weight is above a maximum. What value is this maximum?
  1. (2 pts) What percent of cardinals are less than 83 g?