Respuesta :
Answer:
She needs to sample 189 trees.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The standard deviation of the population is 70 peaches per tree.
This means that [tex]\sigma = 70[/tex]
How many trees does she need to sample to obtain an average accurate to within 10 peaches per tree?
She needs to sample n trees.
n is found when M = 10. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]10 = 1.96\frac{70}{\sqrt{n}}[/tex]
[tex]10\sqrt{n} = 1.96*70[/tex]
Dividing both sides by 10:
[tex]\sqrt{n} = 1.96*7[/tex]
[tex](\sqrt{n})^2 = (1.96*7)^2[/tex]
[tex]n = 188.2[/tex]
Rounding up:
She needs to sample 189 trees.
