Question

In the EAI sampling problem, the population mean is $51,200 and the population standard deviation is $4,000. When the sample size is n = 20, there is a 0.4238 probability of obtaining a sample mean within +/- $500 of the population mean. Use z-table.

1. What is the probability that the sample mean is within $500 of the population mean if a sample of size 40 is used (to 4 decimals)?
     
   
2. What is the probability that the sample mean is within $500 of the population mean if a sample of size 80 is used (to 4 decimals)?

Answer 1

a). the probability that the sample mean is within $500 of the population mean if a sample of size 40 is used = 0.5704

[ interpretation:-

here, sample mean() = population mean = 51200

sample sd () =

so,

the needed probability be:-

[ from standard normal table ]

[using ti 84 plus calculator, you will get,

normalcdf(50700,51700,51200,632.4555)= 0.5708]

b). the probability that the sample mean is within $500 of the population mean if a sample of size 80 is used = 0.7372

[ interpretation:-

here, sample mean() = population mean = 51200

sample sd () =

so,

the needed probability be:-

[ from standard normal table ]

[using ti 84 plus calculator, you will get the more accurate answer that is:-

normalcdf(50700,51700,51200,447.2136)=0.7364 ]

]

**here, as it is instructed to use the z table, i have finalised the hand calculated answer....i have given the calculator provided answer for your clarification.

***If you have any doubt regarding the problem please write it in the comment box...if you are satisfied please give me a LIKE if possible...