Find the slope of the line that passes through (9, 10) and (5, 19). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
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General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (9, 10)

Point (5, 19)

Step 2: Find slope m

a)

b) There is an approximately 2.5% chance that 27 or more teenagers in the group will shop at the mall during the next week.

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Part a

Let X the random variable of interest, on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

The expected value is given by this formula:

And the standard deviation for the random variable is given by:

3) Part b

We need to check if we can use the normal approximation , the conditions are:

and

So then we can apply the normal approximation to the binomial distribution in our case:

We need on the right tail of the distribution a value a that gives to us 2.5% of the area below and 97.5% of the area above. Both conditions are equivalent.  

Let's use the condition , the best way to solve this problem is using the z score with the following formula:  

So we need a value from the normal standard distribution that accumulates 0.025 of the area on the left and 0.975 on the right. This value on this case is -1.96 and we can founded with the following code in excel:  

"=NORM.INV(0.025,0,1)"  

If we apply the z score formula to our case we have this:  

So then based on the equalities we have this:  

And if we solve for a we got:  

There is an approximately 2.5% chance that 27 or more teenagers in the group will shop at the mall during the next week.