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Lubov Fominskaja [6]
3 years ago
10

How to find standard deviation from percentile for normal distribution?

Mathematics
1 answer:
QveST [7]3 years ago
8 0
The standard deviation of what?  Percentiles from any normal distribution look the same, just like the unit normal, so you can't really determine the standard deviation of the original scores. You can determine a z score from a percentile.  That tells us the number of standard deviations, positive or negative, a given score is away from the mean score.  It's a normalized test result.

Your percentile is (a hundred times) the probability that another score is less than your score.  We have a normal distribution, so that probability is the integral of the standard normal from negative infinity to our normalized score.  

Let's call the percentile rank p, already scaled between zero and 1.

p=.5 corresponds to a z score z=0 because the fiftieth percentile means we got an exactly average score, 0 standard deviations away from the mean.

We know 68% of the probability will be between -1 and +1 standard deviation.  So z=-1 corresponds to p=.5-.68/2=.16 and
z=1 corresponds to p=.5+.68/2=.84

Similarly, 95% of the probability will be between -2 and +2 standard deviations.  So z=-2 corresponds to p=.5-.95/2=.025 and
z=2 corresponds to p=.5+.95/2=.975

That's about the list I can do off the top of my head. I think three standard deviations is 99.7%. For the rest we just consult a z table or integrated normal table.  We find p in the body of the table (maybe |.5-p| depending on the table) and then the column headings tell us our z score.

In this modern age, your computer can do this for you quickly

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95% of the students passed the math final exam. If 200 students take the final, how many students passed? Steps greatly apprecia
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A null hypothesis is that the mean nose lengths of men and women are the same. The alternative hypothesis is that men have a lon
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Answer:

b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.

See explanation below.

Step-by-step explanation:

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different (men have longer mean nose length than women), the system of hypothesis would be:

Null hypothesis:\mu_{men} \leq \mu_{women}

Alternative hypothesis:\mu_{men} > \mu_{women}

Assuming that we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:

z=\frac{\bar X_{men}-\bar X_{women}}{\sqrt{\frac{\sigma^2_{men}}{n_{men}}+\frac{\sigma^2_{women}}{n_{women}}}} (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Let's assume that the calculated statistic is z_{calc}

Since is a right tailed test test the p value would be:

p_v =P(Z>z_{calc})=0.225

And we know that the p value is 0.225. If we select a significance level for example 0.05 or 0.1 we see that p_v >\alpha

And on this case we have enough evidence to FAIl to reject the null hypothesis that the means are equal. So then the best conclusion would be:

b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.

8 0
3 years ago
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