Question

If the expected value (the mean) of successes in a binomial experiment of 100 trials is 55. Which of the following are not true?Let x = the no. of successes of the 100 trials. Then P(s) = p = 55/100 = 0.55The standard deviation of the binomial distribution is approximately σ = √(npq) = √(100x0.55x0.45) ≈ 4.97The probability distribution of x = B(100, 0.55) can be approximated by N(55, 4.97)a) I onlyb) II onlyc) I and IId) All of the statements are true

Answer 1

All of the statements are true

Explanation:

Given that :

Number of trials (n) = 100

Expected number of successes = 55

The number of successes of the 100 trials :

Number of successes / number of trials = 55 / 100 = expected number of successes / n = 55/ 100 = 0.55

Using Normal approximation :

Standard deviation (σ) = √(npq) ; q = 1 - p = 1 - 0.55 = 0.45

σ = √(100 * 0.55 * 0.45) = √24.75 = 4.975

The probability distribution of x = B(n, p) = x = B(100, 0.55)

Using approximation ; N(p, σ) = N(55, 4.97)

Hence, All of the statements are true