Question

check my answer please?

.A GE lightbulb is supposed to last for 1,200 hours. In fact, light bulbs of this type last only 1,185 hours with a standard deviation of 70 hours. What is the probability that a sample of 100 lightbulbs will have an average life of at least 1,200 hours?

1 in 2.41

Answer 1

i think your right

Answer 2

yeah

Answer 3

Thank you

Answer 4

first find the probability that an individual lightbulb has a life of at least 1200 hours

Answer 5

@perl do we know the lifetime of a light bulb is normally distributed though?

Answer 6

good point :) , it doesnt say

Answer 7

We can probably assume it in this case, but it doesn't hurt to be careful

Answer 8

so do you agree with my answer?

Answer 9

you need to use the xbar distribution for this one

Answer 10

yes because the sample is size 100

Answer 11

the xbar distribution is the distribution of sample means. You are looking for the area under the curve to the right of x = 1200. This curve is normally distributed with mean = 1185, standard deviation = sigma/sqrt(n) = 70/sqrt(100) = 7

Answer 12

0.214?

Answer 13

$$
\Large
{ P( \bar X \geq 1200) = P( Z_\bar{X} \geq \frac{1200 - 1185}{\frac{70}{\sqrt{100}}} )

\\=P( Z_\bar{X} \geq 2.142857)
}= 0.0160622

$$

Answer 14

I'm getting 0.0161 roughly, so I agree with perl's answer

Answer 15

P(X>1200) = P(Z>0.21428571428571427) = 0.4151621288278977 = 1/2.41 ?

Answer 16

you should have 2.142857 and not 0.2142857

Answer 17

so my answer is 0.0160622

Answer 18

approximately, yes

Answer 19

1/2.41 is too big ... that is 0.4149

Answer 20

K...so my answer is 0.0160622

Answer 21

Is this right?

Answer 22

Thank you, that's what i will put

Answer 23

0.0161 to 4 decimals