Question

A normal population has mean μ-9 and standard deviation σ-5. Round the answers to fou decimal places. Part 1 What proportion of the population is less than 20? The proportion of the population less than 20 is .986 Part 2 out of 2 What is the probability that a randomly chosen value will be greater than 5? The probability that a randomly chosen value will be greater than 5 is

Answer 1

Answer:

a) $P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

b) $P(X\frac{5-\mu}{\sigma})=P(Z>\frac{5-9}{5})=P(z>-0.8)$

And we can find this probability using the complement rule and the normal standard table or excel and we got:

$P(z>-0.8)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(9,5)$  

Where $\mu=9$ and $\sigma=5$

Part a

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

Part b

We are interested on this probability

$P(X>5)$

If we apply the z score formula to our probability we got this:

$P(X\frac{5-\mu}{\sigma})=P(Z>\frac{5-9}{5})=P(z>-0.8)$

And we can find this probability using the complement rule and the normal standard table or excel and we got:

$P(z>-0.8)=1-P(z$