Q. 28 - The Practice of Statistics for AP

Question

The candy machine Suppose a large candy machine has $15\%$ orange candies. Use Figure 7.13 (page 435) to help answer the following questions.

(a) Would you be surprised if a sample of 25 candies from the machine contained 8 orange candies (that's $32\%$ orange)? How about 5 orange candies ( $20\%$ orange)? Explain.

(b) Which is more surprising: getting a sample of 25 candies in which $32\%$are orange or getting a sample of 50 candies in which $32\%$ are orange? Explain.

Step-by-Step Solution

Answer

a. 8 orange candies: Surprising 

b. 5 orange candies: Not surprising

Step 1: Given Information (Part a)

Large candy machine has $=15\%$orange candies

Sample candies$=25$

Machine contained 8 orange candies$(32\%)$

5 orange candies $(20\%)=?$

Step 2: Find the domain and intercepts

Determine the domain, x-intercepts, and y-intercepts.

Step 3: Analyze asymptotes and end behavior

Find vertical, horizontal, and oblique asymptotes.

Step 4: Find critical points and intervals

Compute the derivative, find critical points, and determine increase/decrease intervals.

Step 5: Summarize the graph

Combine all information to describe the graph.

Step 6: Conclude with the answer

a. 8 orange candies: Surprising 

b. 5 orange candies: Not surprising