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STAT 1220090
HOMEWORK 4
Fall
2011
Name: ____________
Score_________
1. Given that the population mean μ = 68 and population standard deviation
σ
= 12, find the
sample mean
μX
and the sample standard deviation
σX
for a random sample of size 50 (round off
to two decimal places.)
(a) 68, 12 (b) 9.62, 12 (c) 9.62, 1.70 (d) 68, 1.70 (e) 68, .24
For questions 2 and 3.
It is known that the mean diameter of pine trees in a national forest is 9.6
(inches) with a standard deviation 2.4 (inches). Assuming that the tree diameters are distributed
normally.
2. If a pine tree is to be selected randomly from this forest, what is the probability that its
diameter will fall between 7.2 inches and 14.4 inches?
(a)
.1359 (b) .6826 (c) .9544 (d) .8185 (e) .9772
3. If a selected pine tree from this forest is at the 90th percentile, what is its diameter (rounded
off to two decimal places) in inches?
(a)
12.67 (b) 14.30 (c) 13.55 (d) 14.69 (e) 18.19
4. Personal best finishing times for a particular race in high school track meets are normally
distributed with mean 5.27 minutes and standard deviation .42 minutes. If the qualifying time for
this event for the regional championship is to be set so that only four percent of all runners
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