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- (ANSWER) MATH 225N WEEK 4 ASSIGNMENT: EVALUATING PROBABILITY WITH THE BINOMIAL DISTRIBUTION

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**Question 1**

The probability of winning on an arcade game is 0.568. If you play the arcade game 22 times, what is the probability of winning more than 15 times?

- Round your answer to three decimal places.

Question 2

Jamie is practicing free throws before her next basketball game. The probability that she makes each shot is 0.6. If she takes 10 shots, what is the probability that she makes exactly 7 of them? Round your answer to three decimal places.

**Question 3**

For the below problem, which values would you fill in the blanks of the function **binompdf(__, __, __)** if you are using a TI-84 graphing calculator?

The probability of saving a penalty kick from the opposing team is 0.617 for a soccer goalie. If 7 penalty kicks are shot at the goal, what is the probability that the goalie will save 5 of them

**Question 4**

65% of the people in Missouri pass the driver’s test on the first attempt. A group of 7 people took the test. Which of the following equations correctly calculate the probability that **at least **3 in the group pass their driver’s tests in their first atempt? Select all that apply.

Remember: 65% = 0.65.

**Question 5**

65% of the people in Missouri pass the driver’s test on the first attempt. A group of 7 people took the test. What is the probability that **at most **3 in the group pass their driver’s tests in their first attempt? Round your answer to three decimal places.

Remember: 65% = 0.65.

**Question 6**

Identify the parameter n in the following binomial distribution scenario. A weighted coin has a 0.449 probability of landing on heads and a 0.551 probability of landing on tails. If you toss the coin 15 times, we want to know the probability of getting heads no more than 8 times. (Consider a toss of heads as success in the binomial distribution.)

**Question 7**

Identify the parameters p and n in the following binomial distribution scenario. A basketball player has a 0.404 probability of making a free throw and a 0.596 probability of missing. If the player shoots 21 free throws, we want to know the probability that he makes no more than 6 of them. (Consider made free throws as successes in the binomial distribution.)

**Question 8**

Identify the parameters p and n in the following binomial distribution scenario. The probability of winning an arcade game is 0.489 and the probability of losing is 0.511. If you play the arcade game 15 times, we want to know the probability of winning more than 8 times. (Consider winning as a success in the binomial distribution.)

**Question 9**

Jackie is practicing free throws after basketball practice. She makes a free throw shot with probability 0.7. She takes 20 shots. We say that making a shot is a success.

What are the values of p, q, and n in this context?

**Question 10**

According to a Gallup poll, 60% of American adults prefer saving over spending. Let X= the number of American adults out of a random sample of 50 who prefer saving to spending.

What is the mean (μ) and standard deviation (σ) of X?

**μ=30 and σ≈3.46**

**Remember that the mean μ is given by the formula μ=np. This should make sense because you can think of p as the fraction of the sample, on average, that will be a success.**

**In this case p=0.6 because we think of a success as someone who prefers saving over spending. n is the size of the sample, 50. So**

**μ=(50)(0.6)=30**

**Standard deviation is given by the formula σ=npq−−−√. As above, n=50 and p=0.6. Remember that p+q=1, so solving for q we find that q=1−p=0.4. So**

**σ=(50)(0.6)(0.4)−−−−−−−−−−−√=12−−√≈3.46**

**Question 11**

Identify the parameters p and n in the following binomial distribution scenario. The probability of winning an arcade game is 0.718 and the probability of losing is 0.282. If you play the arcade game 20 times, we want to know the probability of winning more than 15 times. (Consider winning as a success in the binomial distribution.)

**Question 12**

Identify the parameter n in the following binomial distribution scenario. A basketball player has a 0.429 probability of making a free throw and a 0.571 probability of missing. If the player shoots 20 free throws, we want to know the probability that he makes no more than 12 of them. (Consider made free throws as successes in the binomial distribution.)

**Question 13**

The table below shows a probability density function for a discrete random variable X, the number of times high school students study in the school library per week. What is the probability that X is 2?

- Provide the final answer as a fraction.

x | P(X = x) |

0 | 1/3 |

1 | 1/12 |

2 | 1/12 |

3 | 1/3 |

4 | 1/6 |

**Question 14**

Does the distribution below satisfy the criteria for a discrete probability distribution function?

x | P(X=x) |

0 | 18 |

1 | 14 |

2 | 12 |

3 | 0 |

**Question** 15

The table below shows a probability density function for a discrete random variable X. What is the probability that X is 0?

x | P(X=x) |

0 | 1/14 |

1 | 2/14 |

2 | 7/14 |

3 | 4/14 |

**Question 16**

Identify the parameters p and

n in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.522 and without a popcorn coupon is 0.478. If you buy 24 movie tickets, we want to know the probability that more than 15 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)

Question 17

Identify the parameter n in the following binomial distribution scenario. The probability of buying a movie ticket with a popcorn coupon is 0.657 and without a popcorn coupon is 0.343. If you buy 28 movie tickets, we want to know the probability that exactly 20 of the tickets have popcorn coupons. (Consider tickets with popcorn coupons as successes in the binomial distribution.)

**28**

**The parameters p and n represent the probability of success on any given trial and the total number of trials, respectively. In this case, the total number of trials, or movie tickets, is n=28.**

**Question 18**

Identify the parameters p and n in the following binomial distribution scenario.

Jack, a bowler, has a 0.38 probability of throwing a strike and a 0.62 probability of not throwing a strike. Jack bowls 20 times (Consider that throwing a strike is a success.)

p=0.38,n=20

In a binomial distribution, there are only two possible outcomes. p denotes the probability of the event or trial resulting in a success. In this scenario, it would be the probability of Jack bowling a strike, which is 0.38.

The total number of repeated and identical events or trials is denoted by n. In this scenario, Jack bowls a total of 20 times, so n=20.

**Question 19**

The Stomping Elephants volleyball team plays 30 matches in a week-long tournament. On average, they win 4 out of every 6 matches. What is the mean for the number of matches that they win in the tournament?

**Question 20**

Using the same scenario, what is the standard deviation for the number of matches that they win in the tournament?

The Stomping Elephants volleyball team plays 30 matches in a week-long tournament. On average, they win 4 out of every 6 matches.

**Question 21**

Identify the parameter p in the following binomial distribution scenario. The probability of winning an arcade game is 0.403 and the probability of losing is 0.597. If you play the arcade game 24 times, we want to know the probability of winning more than 7 times. (Consider winning as a success in the binomial distribution.)

**Question 22**

A softball pitcher has a 0.507 probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that more than 8 of them are strikes? (Round your answer to 3 decimal places if necessary.)