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# (Solved) MATH225 Week 4 Assignment – Evaluating Probability with the Binomial Distribution

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Question

A weighted coin has aÂ 0.55Â probability of landing on heads. If you toss the coinÂ 14Â times, what is the probability of getting heads exactlyÂ 9Â times? (Round your answer toÂ 3Â decimal places if necessary.)

Ans.

Â Question

A weighted coin has aÂ 0.455Â probability of landing on heads. If you toss the coinÂ 27Â times, what is the probability of getting heads more thanÂ 12Â times? (Round your answer toÂ 3Â decimal places if necessary.)

Ans.

Question

Identify the parametersÂ pÂ andÂ nÂ in the following binomial distribution scenario. A basketball player has aÂ 0.511Â probability of making a free throw and aÂ 0.489Â probability of missing. If the player shootsÂ 25Â free throws, we want to know the probability that he makes no more thanÂ 10Â of them. (Consider made free throws as successes in the binomial distribution.)

Question

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

Ans.

Question

Give the numerical value of the parameterÂ pÂ in the following binomial distribution scenario.

The probability of buying a movie ticket with a popcorn coupon isÂ 0.629Â and without a popcorn coupon isÂ 0.371. If you buyÂ 29Â movie tickets, we want to know the probability that more thanÂ 16Â of the tickets have popcorn coupons.

Consider tickets with popcorn coupons as successes in the binomial distribution. Do not includeÂ p=Â in your answer.

Question

Identify the parameterÂ pÂ in the following binomial distribution scenario. The probability of winning an arcade game isÂ 0.403Â and the probability of losing isÂ 0.597. If you play the arcade gameÂ 24Â times, we want to know the probability of winning more thanÂ 7Â times. (Consider winning as a success in the binomial distribution.)

• 0.184
• 0.403
• 0.597
• 0.816

Question

Identify the parameter n in the following binomial distribution scenario. A weighted coin has a 0.441 probability of landing on heads and a 0.559 probability of landing on tails.

If you toss the coin 19 times, we want to know the probability of getting heads more than 5 times. (Consider a toss of heads as success in the binomial distribution.)

1. 5
2. 14
3. 19
4. 24

Question

A softball pitcher has aÂ 0.482Â probability of throwing a strike for each pitch. If the softball pitcher throwsÂ 29Â pitches, what is the probability that no more thanÂ 17Â of them are strikes?

Question

A basketball player has aÂ 0.689Â probability of making a free throw. If the player shootsÂ 18Â free throws, what is the probability that she makes no more thanÂ 11Â of them?

Question

The probability of buying a movie ticket with a popcorn coupon isÂ 0.608. If you buyÂ 10Â movie tickets, what is the probability that more thanÂ 3Â of the tickets have popcorn coupons? (Round your answer toÂ 3Â decimal places if necessary)

Question

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

54.4%Â of tickets sold to a movie are sold with a popcorn coupon, andÂ 45.6%Â are not. You want to calculate the probability of selling exactlyÂ 6Â tickets with popcorn coupons out ofÂ 10Â total tickets (orÂ 6Â successes inÂ 10Â trials).

What value should you use for the parameterÂ p?

Question

Give the numerical value of the parameterÂ pÂ in the following binomial distribution scenario.

A softball pitcher has aÂ 0.675Â probability of throwing a strike for each pitch and aÂ 0.325Â probability of throwing a ball. If the softball pitcher throwsÂ 29Â pitches, we want to know the probability that exactlyÂ 19Â of them are strikes.Consider strikes as successes in the binomial distribution. Do not includeÂ p=Â in your answer.

Question

Identify the parametersÂ pÂ andÂ nÂ in the following binomial distribution scenario. The probability of winning an arcade game isÂ 0.718Â and the probability of losing isÂ 0.282. If you play the arcade gameÂ 20Â times, we want to know the probability of winning more thanÂ 15Â times. (Consider winning as a success in the binomial distribution).

Question

Give the numerical value of the parameterÂ pÂ in the following binomial distribution scenario.

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

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

Question

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