Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

**The lifespan of lightbulbs in a photographic machine is normally distributed with a mean of 210 hours and a standard deviation of 50 hours. **

__1) Determine the z-score of a light bulb with a lifespan of exactly 124hours.__

z= x-mean/standard deviation

z= (124-210)/50

x= -1.72

__Z-Score = -1.72__

__2) What is the probability that a randomly chosen light bulb would have a lifespan of less than 180 hours?__

z= x-mean/standard deviation

z= (180-210)/50

z= -0.60

p(x<180) = p(z<-0.60) = 0.2258

__Probability= 0.2258 / 22.58%__

__3) What is the probability that a randomly chosen light bulb would have a lifespan of between 200 and 250 hours?__

z= x-mean/standard deviation FOR BOTH 200 and 250:

**For200:**

z= x-mean/standard deviation

z= (200-210)/50

z= -0.2

**For250:**

z= x-mean/standard deviation

z= (250-210)/50

z= 0.8

p(200<z<250) = p(-0.2<z<0.8) = p(z<0.8) - p(z<-0.2) = 0.7881 -* 0.4207 *= *0.3674 * **Not sure if those italic/underlined numbers are correct on this line**

__Probability = 0.3674 / 36.74%__

Re: Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

Hey tdotodot.

1) is correct

2) is not. Using R we get

> pnorm(-0.6,0,1)

[1] 0.2742531

3) Looks good. Again using R:

pnorm(0.8,0,1) - pnorm(-0.2,0,1)

[1] 0.3674043

Re: Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

Quote:

Originally Posted by

**chiro** Hey tdotodot.

1) is correct

**2) is not. Using R we get**

> pnorm(-0.6,0,1)

[1] 0.2742531

3) Looks good. Again using R:

pnorm(0.8,0,1) - pnorm(-0.2,0,1)

[1] 0.3674043

Thank you, really appreciate your help. Could you tell me how you got 0.2752531 for question #2? And what is "R"?

I am using the Z-Score chart, row 0.6 / column 0.00 shows the number 0.2258 and column 0.01 shows .2291. Other than that, looks good. :)

Re: Can you Check Over MY Work Please - Normal Distribution (Z-SCORE) Word Problem

pnorm(z,0,1) calculates the probability P(Z < z) where Z ~ N(0,1). I used this command to verify your answer.

R is an open source statistical package that is becoming one of the most popular platforms used in statistics.

The R Project for Statistical Computing