If the population proportion p = 0.63, what is the probability of getting correct answers on less than 60% of the questions?

Complete question:

An exam consists of 50 multiple choice questions. Based on how much you studied, for any given question, you think you have a probability of 0.63 of getting the correct answer. Consider the sampling distribution of the sample proportion of correct questions out of 50.

If the population proportion p = 0.63, what is the probability of getting correct answers on less than 60% of the questions?

the probability of getting correct answers on less than 60% of the questions is 0.33

Step-by-step explanation:

Given;

number of samples, n = 50

population proportion, P = 0.63

For normal distribution;

np ≤ 60     and n(1-p) ≤ 60

(50 x 0.63) ≤ 60   and   (1-0.63) ≤ 60

31.5 ≤ 60    and 22.2 ≤ 60

The condition is satisfied, then mean of the distribution is given by;

x = p =  0.63

The standard deviation is given by;

For a  correct answers on less than 60% of the questions

Upper boundary = 0.6

lower boundary = 0

Thus, the probability is given by;

P (p' < 0.6) = 0.33

Therefore, the probability of getting correct answers on less than 60% of the questions is 0.33

49%

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