If the probability that a fluorescent light has a useful life of at least 500 hours is 0.8, find the probability that among 20 such lights
a) exactly 18 will have a useful life of at least 500 hours
b) at least 15 will have a useful life of at least 500 hours

a)Probability( exactly 18 will have a useful life of at least 500 hours

)= 0.1368

b) Probability(at least 15 will have a useful life of at least 500 hours)=0.8042

Step-by-step explanation:

Let X be random variable.It represent the number of light having a usefull life of at least 500 hours 20 fluorescent lights

Lets consider it success if a light has a useful life of at least 500 hours . so  

Probability of a success in each trial is p =0.8

Because of the trials are independent, X has Binomial distribution  with parameters n= 20 and p=0.8

The probability mass function is,

P(X=x)=b(x;20,0.8)

where x=0,1,2,3,4....20

=

................(1)  

A)exactly 18 will have a useful life of at least 500 hours

We Have to find the probability  that exactly 18 will have a useful life of at least 500 hours.

using equation (1)

P(X= 18) =b(18,20,0.08)

P(X= 18)=

P(X= 18)=

P(X= 18)=

P(X= 18)=0.1368

B) at least 15 will have a useful life of at least 500 hours

We Have to find the probability that at least 15 will have a useful life of at least 500 hours

P(X>= 15) = 1-P(X<=14)

P(X>= 15)=1-

P(X>= 15) =

P(X>= 15)=

P(X>= 15)1= -0.1958

P(X>= 15)=0.8042

29.5977692753

step-by-step explanation:

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