Question

Use the normal distribution to the right to answer the questions

(a) What percent of the scores are less than 19? 

(b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21? 

 (a) The percent of scores that are less than 19 is _______ %.

Answer 1

Solution:

(a)

$$ \begin{aligned} &\mathrm{P}(\mathrm{x}<19)=\mathrm{P}[(\mathrm{x}-\mu) / \sigma<(19-20.1) / 5.2] \\ &=\mathrm{P}(\mathrm{z}<-0.21) \\ &=0.4168 \end{aligned} $$

$$ 41.68 \% $$

(b)

$$ \begin{aligned} &\mathrm{P}(\mathrm{x}>21)=1-\mathrm{P}(\mathrm{x}<21) \\ &=1-\mathrm{P}[(\mathrm{x}-\mu) / \sigma<(21-20.1) / 5.2] \\ &=1-\mathrm{P}(\mathrm{z}<0.17) \\ &=0.4325 \end{aligned} $$

Answer = 0.4325 * 1500 = 648.75