marystew3461 marystew3461

13-08-2019
Mathematics

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James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. His staff randomly selected personnel files for 100 tellers in the Southeast Region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 95% confidence interval for the population mean of training times is ________.

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JeanaShupp JeanaShupp

15-08-2019

Answer: (24.02,25.98)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given : Sample size : n= 100

Sample mean : [tex]\overline{x}=25\text{ hours}[/tex]

Standard deviation : [tex]\sigma=5\text{ hours}[/tex]

Significance level : [tex]\alpha: 1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}=1.96[/tex]

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=25\pm(1.96)\dfrac{5}{\sqrt{100}}\\\\=25\pm0.98\\\\=(25-0.98,\ 25+0.98)=(24.02,25.98)[/tex]

Hence, the 95% confidence interval for the population mean of training times is (24.02, 25.98).

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