Question

The amount of orange juice in a 500 ml can from a certain company is a random variable with a mean of 500 ml and a standard deviation of 2 ml. In a sample of size 100, find an approximate probability that the sample mean is less than 499.5 ml (round off to fourth decimal place).

Answer 1

Answer:

0.0062

Step-by-step explanation:

Given that the mount of orange juice in a 500 ml can from a certain company is a random variable with a mean of 500 ml and a standard deviation of 2 ml.

As per central limit theorem sample mean follows normal here with mean = 500 ml and std error - $\frac{2}{\sqrt{100} } \\=0.2$

Sample mean is N(500, 0.2)

Required probability

= probability that the sample mean is less than 499.5 ml

= $P(X<499.5)\\=P(Z<\frac{-0.5}{0.2} )\\= P(Z<-2.5)\\\\ =0.00621$

Rounding off

0.0062