Respuesta :
Answer:
The male students must you measure 'n' = 24
Step-by-step explanation:
Step(i):-
Given Population standard deviation = 2.5 inches
Given the margin of error = 1 inches
Step(ii):-
90% confidence interval of Margin of error is determined by
[tex]M.E = \frac{Z_{\frac{\alpha }{2} } S.D}{\sqrt{n} }[/tex]
[tex]Z_{\frac{0.10}{2} } = Z_{0.05} = 1.96[/tex]
[tex]1 = \frac{1.96 X 2.5}{\sqrt{n} }[/tex]
cross multiplication , we get
√n = 4.9
squaring on both sides , we get
n = 24.01≅ 24
Final answer:-
The male students must you measure 'n' = 24
The total number of male students is 24 and this can be determined by using the formula of margin of error.
Given :
- The average height of young adult males has a normal distribution with a standard deviation of 2.5 inches.
- 90% confidence interval.
The formula of margin of error can be used in order to determine the sample size. The formula of margin of error is given by:
[tex]\rm ME =\dfrac{ Z_{\frac{\alpha }{2}}\times \sigma}{\sqrt{n} }[/tex] ----- (1)
[tex]\rm Z_{\frac{0.1}{2}}=Z_{0.05} = 1.96[/tex]
Now, substitute the known terms in the equation (1).
[tex]\rm 1 =\dfrac{ 1.96\times2.5}{\sqrt{n} }[/tex]
Cross multiply in the above expression.
[tex]\rm \sqrt{n} = 1.96 \times 2.5[/tex]
[tex]\rm \sqrt{n} = 4.9[/tex]
n = 24.01
n [tex]\approx[/tex] 24
So, the total number of male students is 24.
For more information, refer to the link given below:
https://brainly.com/question/2096984
