# MATH399N Week 4 Assignment: Binomial Distribution

## MATH399N Week 4 Assignment: Binomial Distribution

**Question**

65% of the people in Missouri pass the driver’s test on the first attempt. A group of 5 people took the test. What is the probability that less than3in the group pass their driver’s tests in their first attempt? Round your answer to three decimal places.

Remember: 65% = 0.65.

**Question**

A softball pitcher has a 0.431 probability of throwing a strike for each pitch. If the softball pitcher throws 22 pitches, what is the probability that exactly 12 of them are strikes?

- Round your answer to 2decimal places.

**Answer:**

# Question

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 an arcade game as a success in the binomial distribution.)

**Answer:**

**Question**

Give the numerical value of the parameter p in the following binomial distribution scenario.

The probability of winning an arcade game is 0.632 and the probability of losing is 0.368. If you play the arcade game 10 times, we want to know the probability of winning no more than 8 times.

Consider winning as a success in the binomial distribution. Do not include p= in your answer.

**Answer:**

# Question

Consider how the following scenario could be modeled with a binomial distribution, and answer the question that follows.

54.4% of tickets sold to a movie are sold with a popcorn coupon, and 45.6% are not. You want to calculate the probability of selling exactly 6 tickets with popcorn coupons out of 10 total tickets (or 6 successes in 10 trials).

What value should you use for the parameter p?

**Answer:**

**Question**

Give the numerical value of the parameter p in the following binomial distribution scenario.

A softball pitcher has a 0.721 probability of throwing a strike for each pitch and a 0.279 probability of throwing a ball. If the softball pitcher throws 19 pitches, we want to know the probability that more than 15 of them are strikes.

Consider strikes as successes in the binomial distribution. Do not include p= in your answer.

**Answer:**

**Question**

Give the numerical value of the parameter p in the following binomial distribution scenario.

A softball pitcher has a 0.675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If the softball pitcher throws 29 pitches, we want to know the probability that exactly 19 of them are strikes.

Consider strikes as successes in the binomial distribution. Do not include p= in your answer.

**Answer:**

**Question**

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?

- Fill in the blanks with the correct symbol (<, ≤, >, or ≥to represent the correct probability.

**Answer:**

# Question

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 exactly 8 of them are strikes?

Insert the correct symbol to represent this probability.

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