Question

Assume that random guesses are made for seven multiple choice questions on an SAT​ test, so that there are nequals7 ​trials, each with probability of success​ (correct) given by pequals0.55. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4.

Answer 1

Answer: 0.5438

Step-by-step explanation:

Given : Sample size : n=7

Probability of success​ : p=0.55

Using Normal approximation for binomial distribution , we have

$\mu= np =7(0.55)=3.85$

$\sigma=\sqrt{np(1-p)}=\sqrt{7(0.55)(0.45)}=1.32$

The probability that the number x of correct answers is fewer than 4 is given by :-

$P(x$

Hence, the probability that the number x of correct answers is fewer than 4= 0.5438