Question

The duration of electromagnetic pulses (EMP) from solar flares is known to be normally distributed with a mean of 9.2 minutes and a standard deviation of 1.7 minutes.

a) What is the probability an EMP lasts less than 7.40 minutes? %

b) What is the probability an EMP lasts more than 10.10 minutes? %

c) What is the probability of an EMP lasts between 7.40 minutes and 19.30 minutes? % Write your answers in percent form. Round your answers to the nearest tenth of a percent.

Answer 1

Solution :

Given that ,

mean =   = 9.2

standard deviation = = 1.7

P(X< 7.40) = P[(X- ) / < (7.40-9.2) /1.7 ]

= P(z <-1.06 )

Using z table

= 0.1446

=14.46%

b.

P(x >10.10 ) = 1 - P(x< 10.10)

= 1 - P[(x -) / < (10.10-9.2) / 1.7]

= 1 - P(z <0.53 )

Using z table

= 1 - 0.7019

= 0.2981

=29.81%

c0

P(7.40< x <19.30 ) = P[(7.40-9.2) /1.7 < (x - ) / < (19.30-9.2) / 1.7)]

= P( -1.06< Z <5.94)

= P(Z < 5.94) - P(Z <-1.06 )

Using z table   

= 1-0.1446

probability=0.8554