Suppose that 30% of all college freshmen gain weight. A

boitshupoO

boitshupoO

Answered question

2021-09-15

Suppose that 30% of all college freshmen gain weight. A sample of 20 selected randomly. What is the probability that exactly 6 freshmen gain weight?

Answer & Explanation

Clara Reese

Clara Reese

Skilled2021-09-16Added 120 answers

Step 1
The random variable X is the college freshmen gain weight which follows binomial distribution with sample size 20, and probability of success 0.30.
The binomial probability distribution is,
P(X=x)=(beg{array}{c}nxend{array})(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 that exactly 6 freshmen gain weight is,
P(X=6)=(beg{array}{c}206end{array})(0.30)6(10.30)206
=38760×0.00729×0.006782230728
=0.1916
Thus, the probability that exactly 6 freshmen gain weight is 0.1916.

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