Answer to Question #280728 in Statistics and Probability for anor

Question

The manufacturer of a brand of juice drink claims that the mean content of its product is 210 ml with a standard deviation of 6.7 ml.

What is the probability that a randomly selected sample of the product contains more than or equal to 213 ml?

What is the probability that a sample contains less than 200ml?

Answer 1

Given:

Mean $(\mu)=$ 210, Standard deviation $(\sigma)=$ 6.7

Let X be the random variable.

Now,

The probability that a randomly selected sample of the product contains more than or equal to 213 ml is

$P(X>213)=P(\frac{X-\mu}{\sigma}>\frac{213-210}{6.7})=P(Z>0.44)=0.32997$

Hence, The probability that a randomly selected sample of the product contains more than or equal to 213 ml is 0.32997.

Now, the probability that a sample contains less than 200ml is

$P(X<200)=P(\frac{X-\mu}{\sigma}<\frac{200-210}{6.7})=P(Z<-1.49)=0.068112$

Hence, the probability that a sample contains less than 200ml is 0.068112.