Question

2. The lifetime of light bulb is normally distributed with mean of 1400 hours and standard deviation of 200 hours.

a. What is the probability that a randomly chosen light bulb will last for more than 1800 hours?

b. What percentage of bulbs last between 1350 and 1550 hours?

c. What percentage of bulbs last less than 1.5 standard deviations below the mean lifetime or longer than 1.5 standard deviations above the mean?

d. Find a value k such that 20% of the bulbs last longer than k hours.

Answer 1

z table used for P(z<Z) is :

2.

a.

P(x>1800) = 0.0228

b.

P(1350<x<1550) = 0.3721

c.

mean+1.5*SD = 1700

mean-1.5*SD = 1100

P(mean+1.5*SD<x<mean-1.5*SD) = P(1100<x<1700)

P(mean+1.5*SD<x<mean-1.5*SD) = P(1100<x<1700)=0.8664

P(mean+1.5*SD<x<mean-1.5*SD) = 0.8664

d.

P(x>k) = 20%=0.20

P(x<k) = 1-0.20 = 0.80

for this z = 0.84 {from the table}

k=mean+z*sd

= 1400+0.84*200 = 1568

k = 1568

(please UPVOTE)