Question

The duration of electromagnetic pulses (EMP) from solar flares is known to be normally distributed with a mean of 5.7 minutes and a standard deviation of 1.5 minutes.  Write your answers in percent form. Round your answers to the nearest tenth of a percent.

a) What is the probability an EMP lasts less than 4.60 minutes? _____ %
b) What is the probability an EMP lasts more than 6.30 minutes? _____ %
c) What is the probability of an EMP lasts between 4.60 minutes and 12.00 minutes? ______ %

Answer 1

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Answer:

Given that ,

mean =   = 5.7

standard deviation = = 1.5

P(X< 4.6) = P[(X- ) / < (4.6-5.7) /1.5 ]

Using z table

= 0.2317

= 23.17%

b.

P(x >6.3 )

= P[(x -) / > (6.3-5.7) / 1.5]

= 1 - P(z <0.53 )

Using z table

=34.46%

c

P(4.6< x <12 ) = P[(4.6-5.7) /1.5 < (x - ) / < (12-5.7) / 1.5)]

= 0.9999- 0.23169

probability= 76.82%