Question

 

An employee takes time of her trip from her home to office as normally distributed with a mean of 21 minutes and a standard deviation of 7 minutes. What proportion of her trip takes between 25 and 29 minutes? Draw the graph also.

 

Find the probability that standard normal random variable takes on the given values. Show the required area on the graph.

 

Pz=2.5

 

Pz0-Pz<-1.96

 

P-1.05<z

 

P-∞<z<+

 

   2 P0<z<1

 

Answer 1

Given .

Between 25 and 29:

P(25 < X < 29) = ?

We know that the Standard Normal Variate is Z

Therefore P(25 < X < 29) = P(0.57 < Z < 1.14) = ?

Therefore P(0.57 < Z < 1.14) = ?

we have to find out the probability of shaded area

NOTE:

To know the P(0 < Z <0.57); Search the probability value which is intersected between the Z value 0.5 and 0.07

To know the P(0 < Z < 1.14); Search the Probability value which is intersected between the Z values 1.1 and 0.04 in the standard normal tabulated value which is posted below