Answer to Question #282857 in Statistics and Probability for eden

Question

suppose speed of vehicles on a particular stretch of roadway are normally distributed with mean 36.6 mph and standard deviation 1.7 mph. Find the probability that the mean speed of 20 randomly selected vehicles is between 35 and 40 mph on quizlet

Answer 1

Solution;

Given:

Mean=$\mu=36.6mph$

Standard deviation=$\sigma=1.7mph$ .

Using the Z table,

$P(35<x<40)=P[\frac{(35-36.6)}{1.7}<\frac{x-\mu}{\sigma}<\frac{(40-36.6)}{1.7}]$

Simplifying

$=P(-0.9411<z<2)$

Rewrite as

$=P(z<2)-P(z<-0.9411)$

From the tables,

$=0.9772-0.1736$

Probability is

$0.8036$