Question 872104: The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken.
19) Referring to Table 7-4, what is the probability that the sample mean lifetime is more than 1,550 hours? 19) _____________
20) Referring to Table 7-4, the probability is 0.15 that the sample mean lifetime is more than how many hours?
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
mean of 1,600 hours and a standard deviation of 400 hours.
sample 64; s = 400/sqrt(64) = 50
19)P(x > 1550), z = (1550 - 1600)/50 = -50/50 = -1
P(x > 1550) = P(z > -1) = 1 -.1587(area to the left) = .8413 0r 84.13%
20) Referring to Table 7-4, the probability is 0.15 that the sample mean lifetime is more than how many hours?
z =invNorm(.85) = 1.0364
1.0364 = (X - 1600)/50 , 50*1.0364 + 1600 = 51.82+ 1600 = 1652
Below: z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.
z-values indicative of the Area to the left under the curve.
Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right
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