Question

The average cost per household of owning a brand new car is Php 5,000. Suppose that we randomly selected 40 households, determine the probability that the sample mean for these 40 households is more than Php 5,350. Assume that the variable is normally distributed and the standard deviation is Php 1,230.

WHAT IS THE STANDARD ERROR OF THE MEAN ?

Answer 1

Solution

Population mean $\mu=5,000$

Standard deviation $\sigma=1,230$

Sample size $n=40$

Probability that $\bar X >5,350$

$Z=\dfrac{X-\mu}{\sigma/\sqrt n}$

$Z=\dfrac{5,350-5,000}{1,230\times \sqrt {40}}=1.8$

From normal distribution tables

$P(\bar X >5,350) =1-0.964$

$=0.0359$