Normal distribution - Scores on a test are normally distributed with a mean of 75 and a standard deviation of 8. Estimate the probability that a randomly selected student scored between 71 and 75 .

Question

Normal distribution - Scores on a test are normally distributed with a mean of 75 and a standard deviation of 8.  Estimate the probability that a randomly selected student scored between 71 and 75 .

anonymous · Answer

Do you have a z-table with you?

anonymous · Answer

yes , i just dont know how to find a score when its between two numbers like 71 & 75

anonymous · Answer

Okay, the first thing to notice is that $P(71<X<75)$ is equivalent to $P(X<75)-P(X<71)$. In other words, the area between 71 and 75 is the area between 0 (or -$\infty$) and 75 MINUS the area between 0 (or $-\infty$) and 71.

So, what you have to do is find $P(X<75)$ and $P(X<71)$. Do you know how to do that? the transformation to $z$, i mean?

anonymous · Answer

no i dont :(

anonymous · Answer

The transformation is from one random variable $X$, with normal distribution, to another, $Z$ with what's called the standardized normal distribution. The random variables are related by the following:
$$Z=\frac{X-\mu}{\sigma}$$
where $\mu$ is the mean and $\sigma$ is the standard deviation.

This means that $P(X<76)$, for example, is the same as $P(Z<0.125)$, since
$$Z=\frac{76-75}{8}=0.125$$
Checking a z-table, you'll see that the probability of getting a score of 76 is then approximately 55%.

phi · Answer

I would start by sketching a "bell curve" and labeling the region of interest
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