The mean of a population is 74 and the standard deviation is 16. 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 36 yielding a sample mean of 75 or more b. A random sample of size 140 yielding a sample mean of between 72 and 75 c. A random sample of size 217 yielding a sample mean of less than 74.7

a

b

c

Step-by-step explanation:

From the question we are told that

  The population mean is  

  The population standard deviation is  

 Considering question a  

    The sample size is  n  =  36  

Generally the standard error of mean is mathematically represented as

=>  

=>  

Generally the probability that a  random sample of size 36 yielding a sample mean of 75 or more is mathematically represented as

From the z table  the area under the normal curve representing 0.3745 to the right is  

=>  

 Considering question b  

    The sample size is  n  =  104

Generally the standard error of mean is mathematically represented as

=>  

=>  

Generally the probability that a random sample of size 104 yielding a sample mean  between 72 and 75 is mathematically represented as

=>  

=>  

From the z table  the area under the normal curve representing -1.275 to to the left is

=>

=>

Considering question c

    The sample size is  n  =  217

Generally the standard error of mean is mathematically represented as

=>  

=>  

Generally the probability that a  random sample of size 217 yielding a sample mean of less than 74.7 is mathematically represented as

=>  

From the z table  the area under the normal curve representing 0.6446  to to the left is

=>  

i believe it's a.

i'm not sure on this one, most likely correct.