Question

The duration of electromagnetic pulses (EMP) from solar flares is known to be normally distributed with a mean of 5.9 minutes and a standard deviation of 1.1 minutes.
a) What is the probability an EMP lasts less than 4.70 minutes?_____ %
b) What is the probability an EMP lasts more than 6.50 minutes?______%
c) What is the probability of an EMP lasts between 4.70 minutes and 12.40 minutes?______ %
Write your answers in percent form. Round your answers to the nearest tenth of a percent.

Answer 1

solution

Solution :

Given that ,

mean =   = 5.9

standard deviation = =1.1

P(X<4.70 ) = P[(X- ) / < (4.70-5.9) /1.1 ]

= P(z <-1.09 )

Using z table

= 0.1379

probability=0.1379

(B)

P(x > 6.50) = 1 - P(x< 6.50)

= 1 - P[(x -) / < (6.50-5.9) /1.1 ]

= 1 - P(z <0.55 )

Using z table

= 1 - 0.7088

= 0.2912

probability=0.2912

(C)

P(4.70< x < 12.40) = P[(4.70-5.9) / 1.1< (x - ) / < (12.40-5.9) / 1.1)]

= P(-1.09 < Z <5.91 )

= P(Z <5.91 ) - P(Z <-1.09 )

Using z table   

= 1-0.1379

=0.8621

answer=86.2%