9 the manager of a simply sweet bakery surveyed a random sample of the shops customers about their favorite…

9 the manager of a simply sweet bakery surveyed a random sample of the shops customers about their favorite flavor of cupcake. the table shows the number of customers who selected each flavor of cupcake. favorite cupcake flavor chocolate lemon peanut butter red velvet vanilla other 41 29 18 32 22 8 based on the information in the table, which inference about the favorite flavor of cupcake of all of the shops customers appears to be invalid? a. less than one - third are likely to be chocolate cupcake. b. at least half are likely to select a lemon, peanut butter, or red velvet cupcake. c. at least half are likely to select a chocolate or vanilla cupcake. d. one - third are likely to select a red velvet or peanut butter cupcake.

9 the manager of a simply sweet bakery surveyed a random sample of the shops customers about their favorite flavor of cupcake. the table shows the number of customers who selected each flavor of cupcake. favorite cupcake flavor chocolate lemon peanut butter red velvet vanilla other 41 29 18 32 22 8 based on the information in the table, which inference about the favorite flavor of cupcake of all of the shops customers appears to be invalid? a. less than one - third are likely to be chocolate cupcake. b. at least half are likely to select a lemon, peanut butter, or red velvet cupcake. c. at least half are likely to select a chocolate or vanilla cupcake. d. one - third are likely to select a red velvet or peanut butter cupcake.

Answer

Answer:

B. At least half are likely to select a lemon, peanut butter, or red velvet cupcake.

Explanation:

Step1: Calculate total number of customers

$41 + 29+18 + 32+22 + 8=150$

Step2: Analyze Option A

Chocolate: 41. $\frac{41}{150}\approx0.273<\frac{1}{3}$, so A is valid.

Step3: Analyze Option B

Lemon + Peanut Butter+ Red Velvet: $29 + 18+32 = 79$. $\frac{79}{150}\approx0.527$. But this is just a sample - we can't be sure at least half of all customers will choose these. And the sample may not be fully representative. So B is invalid.

Step4: Analyze Option C

Chocolate + Vanilla: $41+22 = 63$. $\frac{63}{150}= 0.42<0.5$, but we are looking at likelihood and the sample gives an indication. It's a reasonable inference.

Step5: Analyze Option D

Red Velvet + Peanut Butter: $32 + 18=50$. $\frac{50}{150}=\frac{1}{3}$, so D is a valid inference.