Question

Suppose that approx. two-thirds of the passenger trains traveling from Newark, New Jersey to Philadelphia, Pennsylvania, are recorded with what appear to be a normal distribution of average speeds that range from 62 to 74 mi/hr. Compute your answers to four decimal places. a/ What is the probability that a train will have an average speed of more than 80 mi/hr? b/ What is the probability that a train will have an average speed of less than 70 and more than 65 mi/hr? c/What is the probability that a train will have an average speed of more than 100 mi/hr?

Answer 1

According to the given question , Suppose that approx. two-thirds of the passenger trains traveling from Newark, New Jersey to Philadelphia, Pennsylvania, are recorded with what appear to be a normal distribution of average speeds that range from 62 to 74 mi/hr.

As the range of the average speeds that range from 62 to 74 mi/hr. therefore the mean of the speeds is

mile/hr.

and the standard deviation is determined as:

Let us define be the event that the average speeds of train with normally distributed with

a) Therefore the probability that a train will have an average speed of more than 80 mi/hr is which is determined as:

  

  

Area above the z=2 is shown as below:

b) Therefore the probability that a train will have an average speed of less than 70 and more than 65 mi/hr is which is determined as:

  

Area is shown as below:

c) Therefore  the probability that a train will have an average speed of more than 100 mi/hr is determined as:

  

  

Area above the z=5 is tends to zero.