Respuesta :
Answer: The number of days would be 7 days.
Step-by-step explanation:
Since we have given that
Variance = 30°
Standard deviation = √30 = 5.47
Mean = 4°
At 95% confidence, z = 1.96
So, number of days that the researcher select to measure the temperature would be
[tex]n=(\dfrac{z\times \sigma}{error})^2\\\\n=(\dfrac{1.96\times 5.42}{4})^2\\\\n=7.053\\\\n=7[/tex]
Hence, the number of days would be 7 days.
Using the z-distribution, it is found that the researcher should select to measure 8 days.
The margin of error of a z-confidence interval is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
- z is the critical value.
- [tex]\sigma[/tex] is the population standard deviation.
- n is the sample size.
The first step is finding the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.
In this problem, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.
For this problem, the variance is of 30º, hence [tex]\sigma = \sqrt{30}[/tex].
The number of days is n for which M = 4, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4 = 1.96\frac{\sqrt{30}}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 1.96\sqrt{30}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{30}}{4}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{30}}{4}\right)^2[/tex]
[tex]n = 7.2[/tex]
Rounding up, the researcher should select to measure 8 days.
A similar problem is given at https://brainly.com/question/14936818
