Answer to Question #280803 in Statistics and Probability for Eming

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

Let $X=$ the volume of juice in a sample: $X\sim N(\mu, \sigma^2).$

Given $\mu=210\ ml, \sigma=6.7\ ml.$

i)

$$P(X\geq 213)=1-P(X<213)$$

$$=1-P(Z<\dfrac{213-210}{6.7})$$

$$\approx1-P(Z<0.44776)\approx0.32716$$

ii)

$$P(X<200)=P(Z<\dfrac{200-210}{6.7})$$

$$\approx P(Z<-1.49254)\approx0.06778$$