Question

The average weight of an apple is 185 grams with a

standard deviation of 13 grams, with an approximately

Normal distribution.

How many grams above average is Christopher’s apple?

How many standard deviations above average is Christopher’s apple?

What percent of apples weigh less than Christopher’s?

What percent of apples weigh more than Christopher’s?

David has an apple that is 1 standard deviation below average weight.

What is the weight of David’s apple?

What percent of apples weigh less than David’s?

What percent of apples weigh more than David’s?

What percent of apples fall between David’s and Christopher’s?

Matt has an apple that is in the top 4% of all apples by weight.

Is Matt’s apple above or below average weight?

What percent of apples weigh less than Matt’s?

What is the standardized value of Matt’s apple?

What is the weight of Matt’s apple?

Peter has an apple sauce-making machine that can only use apples within the middle 95% of weights.

What apple weights can Peter’s machine handle?

Jodie likes oranges better than apples. Her orange juice machine can only use oranges that fall within the middle 95% of weights.

What orange weights can Jodie’s machine handle?

Answer 1

Q1-Q4 related to Christopher's apple are incomplete since weight of Christopher's apple is not given. However I answer this question with the assumption that Christopher's has an apple of weight A grams.

Q1: Then for Christopher's apple total grams above average=(A-185) grams

Q2: For Christopher's apple no. of standard deviations above average=(A-185)/13=z₀, say

Q3:

David:

Q5: weight of David’s apple =185-13=172

Q6: