Normal Distribution

**Jdavis6023** · February 4th 2009, 07:15 AM

Assume you have a normal distribution with a mean of 7.5 and standard deviation of 3.

1. What is the probability that x is greater than 8.5?

2. What is the probability that x is greater than 6.5?

3. What is the probability that x is greater than 3 but less than 5.5?

4. What is the probability that x is less than 7.5?

**Henderson** · February 4th 2009, 08:54 AM

Originally Posted by Jdavis6023

Assume you have a normal distribution with a mean of 7.5 and standard deviation of 3.

1. What is the probability that x is greater than 8.5?

8.5 is 1 away from 7.5, so you are .33 of a standard deviation away from your mean. a normal distribution table gives a value of .1293 for .33, so your probability is 12.93%.

2. What is the probability that x is greater than 6.5?

6.5 is also 1 away from 7.5, but now you're talking about everything greater than something below your mean- you'll have more than half the data. So, instead of .1293, you want .8707 (everything else)

3. What is the probability that x is greater than 3 but less than 5.5?

Find two probabilities here, then subtract.

4. What is the probability that x is less than 7.5?

In a normal distribution, what percent of data are above the mean?

**Moo** · February 4th 2009, 09:00 AM

Hello,

Originally Posted by Jdavis6023

Assume you have a normal distribution with a mean of 7.5 and standard deviation of 3.

Let $Z=\frac{X-7.5}{3}$
Z follows a standard normal distribution.

1. What is the probability that x is greater than 8.5?

$\mathbb{P}(X > 8.5)=\mathbb{P} \left(Z > \frac{8.5-7.5}{3}\right)=1-\mathbb{P} \left(Z<\frac{8.5-7.5}{3}\right)$

2. What is the probability that x is greater than 6.5?

$\mathbb{P}(X > 6.5)=\mathbb{P} \left(Z > \frac{6.5-7.5}{3}\right)=1-\mathbb{P}\left(Z<\frac{6.5-7.5}{3}\right)$

3. What is the probability that x is greater than 3 but less than 5.5?

$\mathbb{P}(3<X<5.5)=\mathbb{P} \left(\frac{3-7.5}{3}<Z <\frac{5.5-7.5}{3}\right)=$ $\mathbb{P} \left(Z<\frac{5.5-7.5}{3}\right)-\mathbb{P}\left(Z<\frac{3-7.5}{3}\right)$

4. What is the probability that x is less than 7.5?

This makes $Z<0$ , which is... ?

Use a z-table : http://www.science.mcmaster.ca/psych...e/z-table2.jpg

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