Question

#7. Suppose the amount of a popular sport drink in bottles leaving the filling machine has anormal distribution with mean 100,5 milliliters (ml) and standard deviation 1.5. If 35 bottles arerandomly selected, find the probability that the mean content is less than 102.1 mL

Answer 1

Apply z-score

Given data

$\begin{gathered} \operatorname{mean}\text{ }\mu\text{ = 100.5} \\ \text{Standard deviation }\sigma\text{ = 1.5} \\ x\text{ = 102.1} \end{gathered}$

Here, we use the normal distribution formula below to calculate the answer.

$\begin{gathered} z\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ \text{Next, substitute the values of }\sigma,\text{ }\mu\text{ and x.} \end{gathered}$$\begin{gathered} z\text{ = }\frac{102.1\text{ - 100.5}}{1.5} \\ z\text{ = }\frac{1.6}{1.5} \\ z\text{ = 1.067} \end{gathered}$

Next, use the normal distribution table to find probability.

From the normal distribution table,

The probability that the mean content is less than 102.1 mL = 0.3554

Final answer = 0.3554