The print on the package of 100-watt General Electric soft-white light-bulbs say

Question

The print on the package of 100-watt General Electric soft-white light-bulbs says that these bulbs have an average life of 750 hours. Assume that the lives of all such bulbs have a normal distribution with a mean of 750 hours and a standard deviation of 55 hours. Find the probability that the mean life of a random sample of 25 such bulbs will be:

a. Greater than 745 hours (4 decimal places)
b. Between 725 and 740 hours (4 decimal places)
c. within 10 hours of the population mean (4 decimal places)
d. less than the population mean by at least 5 hours or more (4 decimal places)

Explanation / Answer

Here, mean = 750 , std.deviation = 55 , n =25

a) p(x > 745)

z = ( x -mean) / (s / sqrt(n))

= ( 745 - 750 ) / ( 55 / sqrt(25))

= -0.45

now,we need to find p(z > -0.45)

p(x > 745 ) = p( z > -0.45) = 0.6753

2)

p( 725 <740)

z =( x - mean) / (s /sqrt(n))

z = p ( (725 - 750) / (55 / sqrt(25) <z < (740 - 750) / (55 / sqrt(25) )

= p ( -2.27 < z < -0.90)

Now, we need to find p ( -2.27 < z < -0.90)

p(725 < x < 740 ) = p ( -2.27 < z < -0.90) = 0.1701

(C)

This means we need to find the probability such that life of bulb lies between 740 and 760 hours

P(740 < X < 760) = P(-0.9091 < z < 0.9091) = 0.6367

(D)

This means we need to find the probability such that life of bulb is below 745 hours

P(X<745) = P(z<-0.4546) = 0.3247

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