38) X is a normally distributed random variable with a standard deviation of 2.0

Question

38) X is a normally distributed random variable with a standard deviation of 2.00. Find the 38) mean of X if 12.71% of the area under the distribution curve lies to the right of 1028. (Note: the diagram is not necessarily to scale.) A) 8.0 B) 7.5 C) 9.6 D) 8.7 39) For a normal distribution with a mean of 7 and a standard deviation of 6, the value 10 39) has a z value of A) 1.5 B) 0.5 C)-0.5 D) 2.5 40) In order to have the standard error of the mean be 15, one would need to take 40) samples from a normally distributed population with a standard deviation of 45. 4)9 B) 81 C)3 D) 27 41) A sample of size 44 will be drawn from a population with mean 31 and standard 41) deviation 11. Find the probability that x will be greater than 33. B)0.1131 A) 0.8869 C) 0.1492 D) 0.1251 42) The average age of doctors in a certain hospital is 45.0 years old. Suppose the 42) distribution of ages is normal and has a standard deviation of 8.0 years. If9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 46.9 years. Assume that the variable is normally distributed. A) 59.8% B) 24.2% C) 75.8% D) 25.8% 43) If the standard deviation of a normally distributed population is 55.0 and we take a 43) sample of size 25, then the standard error of the mean is B) 5.0 A) 2.2 C) 55.0 D) 11.0 44) A sample of size 45 will be drawn from a population with mean 10 and standard 44) deviation 5. Find the probability that x will be greater than 11. B) 0.1170 A) 0.9099 C) 0.0721 D) 0.0901

Explanation / Answer

38) Correct answer: option (A)

39) Z-value = (10-7) / 6 = 0.5
Correct answer: option (B)

40) Sample size = Variance / SE^2 = 45^2 / 15^2 = 9
Correct answer: option (A)

41) P(Xbar > 33) = P(Z> (33-31)/ (11/sqrt(44)) = P(Z > 1.206) = 0.1131
Correct answer: Option (B)

42) P(Xbar < 46.9) = P(Z < (46.9-45)/(8/sqrt(9)) = 0.76192 = 76.19%
Correct answer: Option (C)

43)
SE = 55/sqrt(25) = 11
Correct answer: Option (D)

44)P(Xbar > 11) = P( Z > (11-10)/(5/sqrt(45))) = P(Z > 1.34164) = 0.08986
Correct answer: Option (D) 0.0901

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