Question

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1- The scores of all females’ math test writing in June 2012 had a mean of 63 (in percent). Assume that these scores can be modeled by the Normal distribution with a standard deviation of 10 (in percent).

a) What percentage of females writing the math test had scores above 75%?

b) What math score represents the 96% percentile?

c) What is the probability that at least two of five randomly selected females have test score higher than 75%?

e) Find the probability that math score is between 80 and 90.

Answer 1

Let X denote the scores of all females in math test writing in June 2012. Then

a)

i.e. 11.507%

b)

We want to find 'a' such that

which is the required score.

c)

Let Y denote the number of females scoring higher than 75% in math test writing in June 2012. Then

Required probability =

d)