Question

1. A population has a mean of 60 and a standard deviation of 30. Samples of size 16 are randomly selected. Calculate the standard deviation of the sample distribution X.

2. Samples of size 16 are drawn from a population. the sampling distribution for X has a standard deviation of 0.25. Find the standard deviation of the population.

4. Tires are found to have a mean life of 40,000 miles. The standard deviation is 8000. A sample of 400 is chosen. Find the probability that 40,500 < X.

5. Tires are found to have a mean life of 800 hours. The standard deviation is 50. A sample of 100 is chosen. Find the probability that 40 800 < X < 812.

6. A sample of size 64 is chosen from a population. The sample mean is 50 and the standard deviation is 5. Find the upper limit of the 95% confidence interval for the population mean.

Answer 1

10:30, کاحا ? ( x 2 + Soº) : 17 livery poll" mean = "=60, SD sample = n.11. 30 30 Standard deviation of sample=s= Tir : 7.5 4 s=7.5 27 hiven, n=16; s=0.25 o=s. sn=0.2584 = 1 5=1 347 Siven, H:40,000, r: 8000.,n=400. х 8000 NI MIn) where M: 40.000 Jhoo By contral limit theorem, Zi - 40.000 ,N(91) = P(2>1.25) 4oo - 1-P1251-25): 1-0-8944 P (7 340,500) 0 1051 900. 400 > 40; soo - 40,000 hoo Locore)

50 ñ ~N( 800, en) ic ~ N(800,5) sy Livery M=800, so, n=100 X-800 N10,d) S el 800<*<812) 800-800 5 BY CLT, z = 8-3 . Rapome_912160) = P(0<2<24) pl < P1242-4) - P(ZCO) 0.4918.-0.500 P1300 <12812)=0-1918 1) Girer, n=64, X=50, s=5. 95% considence Interval for pool" mean M is, CI:te here te tappt 1.1.948, a=0.05 : 504 1.998 x 198 Xenon = So I 1-244 -148.751, 51.254) (I for M's upper limit is '51.249 so, 95%
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