Answer to Question #343589 in Statistics and Probability for curties

Question

The daily net profit for spaza shop follows a normal distribution with a mean of R220 and a standard deviation of R175.

a) The probability that the daily net profit exceeds R250 is (answer to 2 decimal places)   

b) The cut-off value for lowest 40 % of daily net profits is (in Rands and cents) 

 

Answer 1

a)

$$P(X>250)=1-P(Z\le\dfrac{250-220}{175})$$

$$\approx1-P(Z\le0.1714)\approx0.43$$

b)

$$P(X<x)=P(Z<\dfrac{x-220}{175})=0.4$$

$$\dfrac{x-220}{175}=-0.2533$$

$$x=220-175(0.2533)$$

$$x=175.67$$