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padilas [110]
3 years ago
8

I need help to find the circumstance

Mathematics
1 answer:
ikadub [295]3 years ago
4 0
A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d)
Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).
The circumference of a circle is found using this formula:
C=π⋅D or C=2π⋅R
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A sample from a population with μ = 40 and σ = 8 has a mean of M = 36. If the sample mean corresponds to a z = –1.00, then how m
juin [17]

Answer:

There are 4 scores in the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 40, \sigma = 8, X = 36, Z = -1, s = \frac{8}{\sqrt{n}}

We want to find n. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

-1 = \frac{36 - 40}{\frac{8}{\sqrt{n}}}

-4\sqrt{n} = -8

4\sqrt{n} = 8

Simplifying by 4

\sqrt{n} = 2

(\sqrt{n})^2 = 2^2

n = 4

There are 4 scores in the sample.

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Answer:

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