Answer to Question #307151 in Statistics and Probability for Johan

Question

The amount of sweetener used in a liter of milk tea is a normally distributed with a mean of 0.75 cup and a standard deviation of 0.6 cup. 

a. Suppose 10 liters of milk tea are randomly selected, what is the probability that it will have at least a cup of sweetener?

b.Suppose 20 liters of milk tea are randomly selected, what is the probability that it will have less than half a cup of sweetener?

c.15 liters of milk tea is randomly selected, what is the probability that it will have 0.50 to 1.25 cups of sweetener?

Answer 1

Mean ($\mu$) = 0.75

Standard deviation ($σ$) = 0.6

(a) at least 1 Cup

$Z=\dfrac{X-\mu}{σ}$

$Z=\dfrac{1-0.75}{0.6}$

$= 0.4166$

From the standard normal distribution tables

$Z(1)=0.6591$

Probability of at least 1 Cup

$P=1-0.6591 = 0.3409$

(b) Less than 0.5 cup

$Z=\dfrac{X-\mu}{σ}$

$Z=\dfrac{0.5-0.75}{0.6}$

$Z=-0.4166$

From the standard normal distribution tables probability of less than 0.5 cups

$P(0.5)=0.3409$

(c) Between 0.5 and 1.25

$Z(1.25)=\dfrac{1.25-0.75}{0.6}=0.8333$

$Z(0.5)=-0.4166$

From the standard normal distribution tables probability of between 0.5 and 1.25 cups is:

$=1-[P(0.5)+P(1.25)]$

$=1-[0.3409+0.20327]$

$=0.45583$