Question

QUESTION 9 On average, Stephanie reads 20 page each night with a standard deviation of 5 pages. What is the probability that Stephanie will read at least 20 pages tonight? There is a 50% chance that she will read at least 20 pages tonight. There is a 75% chance that she will read at least 20 pages tonight. ○There is a 95% chance that she will read at least 20 pages tonight. O There is a 25% chance that she will read at least 20 pages tonight.

Answer 1

Let X be the random variable denoting the number of pages Stephanie will read tonight.

Hence, X ~ N(20, 5) i.e. (X - 20)/5 ~ N(0,1).

The probability that Stephanie will read at least 20 pages tonight = P(X $\leq$ 20) = P[(X - 20)/5 $\leq$ (20 - 20)/5] = P[(X - 20)/5 $\leq$ 0] = $\Phi$(0) = 0.5.

[$\Phi$(.) is the cdf of N(0,1)].

Hence, there is a 50% chance that she will read at least 20 pages tonight. (Ans).