Question

question #3
which of the following descriptions best describes the effect of increasing a sample size in a sampling distribution?
o the distribution will get shorter.
o the distribution will get wider.
o the distribution will get narrower.
o none of these.

question #4
a factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. a sample of 100 sheets of glass is to be measured and the mean thickness of the 100 sheets is to be computed. what is the probability that the average thickness of the 100 sheets is less than 4.2 mm?
o.8186
o.3183
o.9655
o.6817

Explanation:

Step1: Calculate the standard error

The formula for the standard error \(SE=\frac{\sigma}{\sqrt{n}}\), where \(\sigma = 1.1\) (population standard deviation) and \(n = 100\) (sample size).

$$SE=\frac{1.1}{\sqrt{100}}=\frac{1.1}{10}=0.11$$

Step2: Calculate the z - score

The formula for the z - score is \(z=\frac{\bar{x}-\mu}{SE}\), where \(\bar{x}=4.2\) (sample mean), \(\mu = 4\) (population mean) and \(SE = 0.11\) (standard error).

$$z=\frac{4.2 - 4}{0.11}=\frac{0.2}{0.11}\approx1.82$$

Step3: Find the probability

Using the standard normal distribution table (or a calculator with a normal - distribution function), we find \(P(Z<1.82)\).
Looking up \(z = 1.82\) in the standard normal table: the value is \(0.9656\approx0.9655\)

Answer:

.9655