The mean of a population is 77 and the standard deviation is 14. The shape of th
ID: 3336361 • Letter: T
Question
The mean of a population is 77 and the standard deviation is 14. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. Appendix A Statistical Tables a. A random sample of size 34 yielding a sample mean of 82 or more b. A random sample of size 120 yielding a sample mean of between 74 and 80 c. A random sample of size 220 yielding a sample mean of less than 77.4 (Round all the values of z to 2 decimal places and final answers to 4 decimal places.) a.
Explanation / Answer
A) P(X > 82) = P((X - mean)/(SD/sqrt (n)) > (82 - 77)/(14 /sqrt(34))
= P(Z > 2.08)
= 1 - P(Z < 2.08)
= 1 - 0.9812 = 0.0188
B) P(74 < X < 80) = P((74 - 77)/(14/sqrt (120)) < Z < (80 - 77)/(14/sqrt(120))
= P(-2.35 < Z < 2.35)
= P(Z < 2.35) - P(Z < -2.35)
= 0.9906 - 0.0094 = 0.9812
C) P(X < 77.4) = P(Z < (77.4 - 77)/(14/sqrt (220))
= P(Z < 0.42)
= 0.6628
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