If a binomial distribution applies with a sample size of n = 20, find the values

Question

If a binomial distribution applies with a sample size of n = 20, find the values below. a The probability of 5 successes if the probability of a success is 0.50 b. The probability of at least 7 successes if the probability of a success is 0.35 c. The expected value, n = 20, p = 0.60 d. The standard deviation, n = 20, p = 0.60 a. The probability of 5 successes if the probability of a success is 0.50 is (Round to four decimal places as needed.) b. The probability of at least 7 successes if the probability of a success is 0.35 is (Round to four decimal places as needed.) c. The expected value is (Type an integer or a decimal.) d. The standard deviation is (Round to four decimal places as needed.)

Explanation / Answer

n=20

a) P(5 successes)=10C5*(0.5)^5*(0.5)^15 =0.01478

b) P(atleast 7 sucesses)=0.01478

c) Mean is n*p or is expected value =20*0.35=7

d) standard deviation is sqrt(n*p*(1-p))=sqrt(0.35*0.65*20)=2.133

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