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Sedbober [7]
3 years ago
15

A study of peach trees found that the average number of peaches per tree was 725. The standard deviation of the population is 70

peaches per tree. A scientist wishes to find the 95% confidence interval for the mean number of peaches per tree. How many trees does she need to sample to obtain an average accurate to within 10 peaches per tree
Mathematics
1 answer:
TEA [102]3 years ago
3 0

Answer:

She needs to sample 189 trees.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.025 = 0.975, so Z = 1.96.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma 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 \sigma = 70

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

M = z\frac{\sigma}{\sqrt{n}}

10 = 1.96\frac{70}{\sqrt{n}}

10\sqrt{n} = 1.96*70

Dividing both sides by 10:

\sqrt{n} = 1.96*7

(\sqrt{n})^2 = (1.96*7)^2

n = 188.2

Rounding up:

She needs to sample 189 trees.

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Bella saw that 7 out of 11 people brought an umbrella to the beach. There 99 people there. How many of them did not have a beach
Alinara [238K]
Hello!

7 out of 11 people brought an umbrella to the beach

this is a fraction of 7/11

We multiply this by 99 to get how many people brought an umbrella out of 99

7/11 * 99 = 63

You subtract this from 99 to see how many did not have an umbrella

99 - 63 = 36

The answer is 36 people

Hope this helps!
7 0
3 years ago
What is the relationship between 9.125 x 10^-3 and 9.125 x 10^2
nalin [4]

9.125*x^2 is 100000 times greater than 9.125*10^(-3).

Note that (10^5)(9.125*10^(-3) = 9.125*10^2.

5 0
2 years ago
Which of the following is a valid exclusion for the algebraic expression
zheka24 [161]

Answer:

4a^2b-8ab^2

Step-by-step explanation:


3 0
2 years ago
2y+5x=4<br> please answer
marshall27 [118]

Answer:x=x=

−2

5

y+

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5

Step-by-step explanation:

Let's solve for x.

2y+5x=4

Step 1: Add -2y to both sides.

5x+2y+−2y=4+−2y

5x=−2y+4

Step 2: Divide both sides by 5.

5x

5

=

−2y+4

5

x=

−2

5

y+

4

5

Answer:

x=

−2

5

y+

4

5

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5 0
2 years ago
Carlos takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $ 98 per cre
Sholpan [36]

Answer:

x + y = 13

98x + 115y = z

Step-by-step explanation:

Let x represent the time spent taking class in Westside community college

Let y represent the time spent taking class in Pinewood community college

Let z represent the combined total amount paid for the class fees.

The total combined time for the two school is given as:

x + y = 13.

For the combined total amount; we multiply the price for each school with the time spent on the school and sum them together.

Westside: 98 * x = 98x

Pinewood: 115 * y = 115y

The combined total amount represented as z is given as:

z = 98x + 115y

7 0
3 years ago
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