Answer to Question #245278 in Statistics and Probability for Leone

Question

The width of white board markers manufactured by a company is approximately normally distributed with a mean of 12 mm (millimetres) and a standard deviation of 4 mm. If a random sample of size 16 white board markers is selected, what is a) the distribution of the mean? b) the probability that the sample mean is less than 15.6 mm? c) the probability that the sample mean is between 12.8 mm and 13.2 mm?

Answer 1

Given problem follows a normal distribution

with mean = 12 mm; standard deviation = 4 mm and n= 16

a)

$Std = \frac{4}{\sqrt{16}}=1 mm$

b)

$P( \bar{x}<15.6)= P(Z<\frac{15.6-12}{\frac{4}{\sqrt{16}}})=P(Z<3.6)=0.9998$

c)

$P( 12.8<\bar{x}<13.2)= P(\frac{12.8-12}{1}<Z<\frac{13.2-12}{1})=P(0.8<Z<1.2)=0.0968$