Question

The population mean weight of a candy is 10 grams with a standard deviation of 2 grams. A sample of 100 candies is taken. What is the probability that the sample mean differs from the population mean by at most 0.3 gram?

Answer 1

Given:

$\mu=10\\\sigma=2\\n=100\\$

ind the probability that the mean of a sample of size 100 will differ from the population mean 10 by at most 0.3 unit, that is, is either more than 9.7 or less than 10.3The corresponding z-value needed to be computed

Formula: $Z= \frac{\overline{X}-\mu}{\frac{\sigma }{\sqrt{n}}}$ = $\frac{9.7-10}{\frac{2 }{\sqrt{100}}}$ = -1.5

Z= $\frac{10.3-10}{\frac{2 }{\sqrt{100}}}$ =1.5

Using z table,$Pr(9.7≤ \overline{X} ≤10.3)$ $=Pr(−1.5≤Z≤1.5)$

$=Pr(Z≤1.5)−Pr(Z≤−1.5)$

=0.9332−0.0668=0.8664