Question

The amount of money a family spends in Florida per week on groceries is normally distributed with a mean of 300 and a standard deviation of 43. Find the following population percentages using z-score

a) z-score of -1.5
b) z-score of 0
c) z-score of 2.5

Options:
A) 6.68%, 50%, 99.38%
B) 10.66%, 68.27%, 99.38%
C) 6.68%, 34.13%, 99.38%
D) 10.66%, 50%, 99.38%

Answer 1

For a normally distributed variable, the areas under the curve corresponding to z-scores of -1.5, 0, and 2.5 are approximately 6.68%, 50%, and 99.38% respectively, which correspond to option A.

Step-by-step explanation:

In the question, we're asked to find population percentages based on z-scores for a normally distributed family grocery spending in Florida with a mean of $300 and a standard deviation of $43.

• a) The z-score of -1.5 corresponds to the left tail of the distribution. About 6.68% of the population falls below this z-score, according to the z-table.
• b) A z-score of 0 is the mean, which divides the distribution exactly in half, so 50% of the values are below this score, and 50% are above.
• c) A z-score of 2.5 is in the upper tail of the distribution. Around 99.38% of the population scores below this z-score, per the z-table.

Therefore, the correct percentages are 6.68% for a z-score of -1.5, 50% for a z-score of 0, and 99.38% for a z-score of 2.5. The correct option is A) 6.68%, 50%, 99.38%.