Answer to Question #163814 in Statistics and Probability for Zafar

Question

Cut fruit is packed for sale in a supermarket. The weights of packages are normally distributed with a mean of 201.49 grams and variance of 24.63 grams.

Given that 5% of the distribution lies below the Z value of -1.64485, find the package weight that has 5% of the distribution above it. Give your result correct to four decimal places.

Answer 1

Given $P(Z<-1.64485)=0.05.$ Then $P(Z>1.64485)=0.05.$

$$Z=\dfrac{X-\mu}{\sigma}$$

Given $\mu=201.49\ g, \sigma=24.63\ g.$

Then

$$\dfrac{X-201.49}{24.63}=1.64489$$

$$X=1.64489(24.63)+201.49\approx242.0036$$

$242.0036$ grams.