Question

6. The average number of chocolate chips in a particular brand of chocolate chip chewy cookie is 19. The standarddeviation is 2.6. Assuming that the number of chocolate chips per cookie is normally distributed, what percentage ofcookies would have between 13.8 and 24.2 chips?

Answer 1

SOLUTION:

Step 1:

In this question, we are given the following:

The average number of chocolate chips in a particular brand of chocolate chip chewy cookie is 19.

The standard deviation is 2.6.

Assuming that the number of chocolate chips per cookie is normally distributed, what percentage of cookies would have between 13.8 and 24.2 chips?

Step 2:

The details of the solution are as follows:

$From\text{ the question, we can see that the formulae for z-score is given as :}$

PART TWO:

From the formulae, we can see that:

$Z_{13.8}=\frac{13.8\text{ - 19}}{2.6}=\frac{-5.2}{2.6}=-2$



$Z_{24.\text{ 2}}=\frac{24.2\text{ -19}}{2.6}=\frac{5.2}{2.6}=2$

PART THREE:

Next, we find the probability between the two z- scores ( -2 and 2) and it is as shown below:

PART FOUR:

What percentage of cookies would have between 13.8 and 24.2 chips?

$P(\text{ -2< X < 2 \rparen = 0.9545}$

Then the percentage would be:

$0.9545\text{ x 100 \% = 95.45 \%}$

CONCLUSION:

The percentage of cookies would have between 13.8 and 24.2 chips = 95. 45 %