Answer:
68 readings.
Explanation:
We need to take this problem as a statistic problem where the normal distribution table help us.
We can start considerating that X is the temperature of the solution, then
[tex]0.9 = P(|\bar{x}-\mu|<0.1)[/tex]
[tex]0.9 = P(\frac{|\bar{x}-\mu|}{\frac{\sigma}{\sqrt{n}}}<\frac{0.1}{\frac{\sigma}{\sqrt{n}}})[/tex]
[tex]0.9 = P(|Z|<\frac{0.1}{\frac{\sigma}{\sqrt{n}}})[/tex]
For a confidence level of 90% our [tex]Z_{critic}[/tex] is 1.645
Therefore,
[tex]\frac{0.1}{\frac{\sigma}{\sqrt{n}}} = 1.645[/tex]
Substituting for [tex]\sigma = 5[/tex] and re-arrange for n, we have that n is equal to
[tex]n=(\frac{1.645\sigma}{0.1})^2[/tex]
[tex]n=\frac{(1.645)^2(0.5)^2}{0.1^2}[/tex]
[tex]n=67.65[/tex]
[tex]n=68[/tex]
We need to make 68 readings for have a probability of 90% and our average is within [tex]0.1\°\frac[/tex]
