1.) The life of light bulbs is distributed normally. The standard deviation of t

Question

1.) The life of light bulbs is distributed normally. The standard deviation of the lifetime is 12 hours and the mean lifetime of a bulb is 520 hours. (Hint: Draw each picture)

a. Find the probability of a bulb lasting for less than 535 hours. (Round your answer to 4 decimal places)

b. Find the probability of a bulb lasting for longer than 541 hours. (Round youranswer to 4 decimal places)

c. Find the probability of a bulb lasting for between 514 and 529 hours. (Roundyour answer to 4 decimal places)

Explanation / Answer

standard deviation of the lifetime is 12 hours and the mean lifetime of a bulb is 520 hours.

find z scores

a) z = ( 535 - 520)/12 = 1.25

P(z<1.25) = 0.8944

b) z = ( 541 - 520)/12 = 1.75

P( z> 1.75) = P ( Z>1.75 ) = 1P ( Z<1.75 ) = 1 0.9599   =   0.0401

c) z1 = (514 - 520)/12 = -0.5 ; z2 =( 529 -520)/12 = 0.75

P( -0.5<z < 0.75) = 0.4649

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