Given:
Mean = 45
Standard deviation = 9
Confidence level = 95%.
To find:
The confidence interval.
Solution:
The formula for confidence interval is:
[tex]C.I.=\overline{x}\pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
Where, [tex]\overline{x}[/tex] is mean, z is the z-value at given level of confidence, [tex]\sigma[/tex] is the standard deviation and n is the number of observations.
The z-value at 95% confidence level is 1.96.
Here number of observations are not given. Assume it is 1.
Putting [tex]\overline{x}=45,\sigma=9,z=1.96,n=1[/tex].
[tex]C.I.=45\pm 1.96\dfrac{9}{\sqrt{1}}[/tex]
[tex]C.I.=45\pm 1.96(9)[/tex]
[tex]C.I.=45\pm 17.64[/tex]
It can be written as
[tex]C.I.=[45-17.64,45+17.64][/tex]
[tex]C.I.=[27.36,62.64][/tex]
Approximate the value to the nearest whole number.
[tex]C.I.=[27,63][/tex]
The interval for the middle 95% of snowfall is 27 to 63.
Therefore, the correct option is A.
