Answer:
The required amount of mice is 11.82 gram.
Step-by-step explanation:
Given : Assuming that it is known from previous studies that σ = 4.5 grams. If we wish to be 95% confident that the mean weight of the sample will be within 3 grams of the population mean for all mice subjected to this protein diet.
To find : How many mice should be included in our sample?
Solution :
The formula used in the situation is
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where, z value at 95% confidence interval is z=1.96
[tex]\mu=3[/tex] gram is the mean of the population
[tex]\sigma=4.5[/tex] gram is the standard deviation of the sample
Substituting the value, to find x sample mean
[tex]1.96=\frac{x-3}{4.5}[/tex]
[tex]1.96\times 4.5=x-3[/tex]
[tex]8.82=x-3[/tex]
[tex]x=8.82+3[/tex]
[tex]x=11.82[/tex]
Therefore, The required amount of mice is 11.82 gram.
