A stock's price fluctuations are approximately normally distributed with a mean of $104.50 and a standard deviation of $23.62. You decide to purchase whenever the price reaches its lowest 10% of values. What is the most you would be willing to pay for the stock? a) $80.88
b) $74.23
c) $84.62
d) $134.77

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]

And if we solve for a we got

And the best answer for this case would be:

b) $74.23

Step-by-step explanation:

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

Where and

For this part we want to find a value a, such that we satisfy this condition:

  (a)

  (b)

As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.282. On this case P(Z<-1.282)=0.10 and P(z>-1.282)=0.90

If we use condition (b) from previous we have this:

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]

And if we solve for a we got

And the best answer for this case would be:

b) $74.23