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?
Answer:
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;
[tex]\sigma_p =\sqrt{\frac{P(1-P)}{n} }\\\\ \sigma_p =\sqrt{\frac{0.63*0.37}{50} }\\\\ \sigma_p = 0.068[/tex]
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
