# 1. Asample of size 75 will be drawn  from a population with mean 10 and standard deviation 12.a. Find the probability that mean will be between 8 and 14.b. Find the 15th percentile of mean.2. A sample of size 20 will be drawn from a population with mean 6 and standard deviation 3.a. Is it appropriate to use the normal distribution to find probabilities for mean?b. If Appropriate find the probability that mean will be greater than 4.c. If appropriate find the 30th percentile of mean.

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1. Asample of size 75 will be drawn  from a population with mean 10 and standard deviation 12.

a. Find the probability that mean will be between 8 and 14.

b. Find the 15th percentile of mean.

2. A sample of size 20 will be drawn from a population with mean 6 and standard deviation 3.

a. Is it appropriate to use the normal distribution to find probabilities for mean?

b. If Appropriate find the probability that mean will be greater than 4.

c. If appropriate find the 30th percentile of mean.

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Step 1

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Given Data

n = 75

mean =10

standard deviation =12

Step 2

a) probability that mean will be between 8 and 14 help_outlineImage TranscriptioncloseP(8 X 14) = Changing into standard normal variate Р(X < 14) — Р(X < 8) 8 10 14 10 14 P 8 H _ - Pz = P z < о 12 12 Vn /75 /75 Р(2 < 2.887) — P(z <-1.443) (P(z 2.887) = 0.998055 From excel (P(z <-1.443) = 0.07451 From excel NORM. S. DIST (2.887, TRUE) NORM. S. DIST(-1.443, TRUE) 0.998055 0.07451 0.923545 probability that mean will be between 8 and 14 = 0.923 fullscreen
Step 3

b) 15th percentil... help_outlineImage Transcriptionclose= 0.15 P (0.15) 1.03643 12 10 8.564 75 X 1.03643 x 15th percentile of mean = 8.564 fullscreen

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