A random sample is drawn from a population with mean -68 and standard deviation

Question

A random sample is drawn from a population with mean -68 and standard deviation -57. Use Table 1. a. Is the sampling distribution of the sample mean with n - 16 and n 41 normally distributed? O Yes, both the sample means will have a normal distribution. O No, both the sample means will not have a normal distribution. O No, only the sample mean with n -16 will have a normal distribution. No, only the sample mean with n 41 will have a normal distribution. b. Can you use the standard normal distribution to calculate the probability that the sample mean falls between 68 and 71 for both sample sizes? O Yes, for both the sample sizes, standard normal distribution could be used. O No, for both the sample sizes, standard normal distribution could not be used. 16, standard normal distribution could be used. No, only for the sample size with n O No, only for the sample size with n = 41, standard normal distribution could be used. Calculate the probability that the sample mean falls between 68 and 71 for n-41. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) c. Probability

Explanation / Answer

A sample size of 30 or more values is large enough for the Central Limit Theorem to be effective.

(a)OptionD

No, only the sample mean with n = 41 will have a normal distribution.

(b)Option D

No, only for the sample size with n = 41, standard normal distribution could be used.

(c)

Given population mean = 68

Population SD= = 5.7

sample size=n=41

sample sd=s= /sqrt(n)=5.7/sqrt(41)

=0.8902

need to find P(68<X<71)?

convert X to Z scores by the formula

  P(68<X<71)=P(Z<71)-P(Z<68)

=P(Z<71-68/0.8902)-P(Z<68-68/0.8902)

=P(Z<3.370029207)-P(Z<0)

=0.9996-0.50

=0.4996

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