Give the numerical value of the parameter p in the following binomial distributi

Nann

Nann

Answered question

2021-09-29

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 & Explanation

Alara Mccarthy

Alara Mccarthy

Skilled2021-09-30Added 85 answers

Step 1
Let X be the number of winning an arcade game which follows binomial distribution with sample size 10, and probability of success (p) 0.632.
Thus, the numerical value of the parameter p is 0.632.
The binomial probability distribution is,
P(X=x)=(nx)(p)x(1p)nx
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
Step 2
The probability of winning no more than 8 times is,
P(X8)=1P(X>8)
=1[P(X=9)+P(X=10)]
K=1[(109)(0.632)9(10.632)109+(1010)(0.632)10(10.632)1010]
=1(0.0592+0.0102)
=10.0694
=0.9306
Thus, the probability of winning no more than 8 times is 0.9306.

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