NormalDistributions DoNow 1. The Dexter company manufactures a new kind of light

Question

NormalDistributions DoNow 1. The Dexter company manufactures a new kind of light bulb based on the technology. The (population) mean life of a Dexter bulb is 7.0 years with a population standard an life of a Dexter bulb is normally distributed. (a) what proportion of Dexter bulbs will last more than 95 years? (b) What proportion of Dexter bulbs will last less than 4.0 years? (c) What proportion of Dexter bulbs will last between 8.0 and 9.0 years? (d) A Dexter bulb that lasts exactly 7.0 years, would be at what percentile? (e) Calculate the 90th percentile for a Dexter bulb. (f) Calculate the 28h percentile for a Dexter bulb.

Explanation / Answer

Solution:- Given that mean = 7 , sd = 1.4

a) P(X > 9.5) = P(Z > (x - )/)
= P(Z > (9.5 - 7.0)/1.4)
= P(Z > 1.79)
= 0.0367

b) P(X < 4) = P(Z < (4 - 7)/1.4)
= P(Z < -2.14)
= 0.0162

c) P(8 < X < 9) = P((8-7)/1.4 < Z < (9-7)/1.4)
= P(0.714 < Z < 1.43)
= 0.1613

d) P(X = 7 ) = P(Z < 0)
= 0.5
= 50%

e) P(Z < (X - 7)/1.4) = 0.90
X - 7 = 1.28*1.4
X = 7 + (1.28*1.4)
X = 8.792

f) P(Z < (X - 7)/1.4) = 0.28
X - 7 = -0.583*1.4
X = 7+(-0.583*1.4)
X = 6.1838

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