Applicant Scores

Question 1

Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100.

4 marks    a. What is the probability that a randomly selected applicant scores between 425 and 575?

4 marks    b. What is the probability that a randomly selected applicant scores 625 or more?

2 marks    c. What is the probability that a randomly selected applicant scores less than 500?

4 marks    d. Twenty per cent of test scores exceed what value?

Question 2

4 marks    The life span of a DVD player produced by one major company is known to be normally distributed with a mean of 6.2 years. If 4.01% of these DVD players have a life span of more than 8 years, what is the standard deviation of the DVD player’s life span?

Question 3

It is estimated that, in jury trials, the jury will reach the correct decision (guilty or not guilty) 92% of the time. In 200 randomly selected jury trials,

4 marks    a. what is the probability that the jury will reach the correct decision in at least 175 of the trials?

3 marks    b. what is the probability that there will be fewer than 180 correct decisions?

4 marks   c. What is the probability that there will be exactly 184 correct decisions?