Question

The weights of apples in a shipment from Al's Orchards are normally distributed with a mean of 142 grams and a standard deviation of 9 grams. The weights of apples in a shipment from Zippy's Orchards are normally distributed with a mean of 165 grams and a standard deviation of 13 grams.

A rotten apple has a mean of 156 grams. Was it more likely to come from Al's or from Zippy's? Use z-scores to explain. Show your work.

I really need some assistance getting started with this question. I would appreciate anyone who can help! :) Thank You

Answer 1

Is this a test?

Answer 2

No. It is a question on my review for the final exam. I am preparing to take the final and I am stuck on this question. I am just looking for some assistance in getting started.

Answer 3

distribution1 :
mean = 142
standard deviation = 9
observation = 156
zscore = ?

distribution2 :
mean = 165
standard deviation = 13
observation = 156
zscore = ?

Answer 4

Opps dont look at distribution 2

Answer 5

\[z=\frac{ x-\mu }{ \sigma }\]
Use that to calculate the z-score for each distribution. The x is 156 for both, µ is the mean, and σ is standard deviation, as noted by @littleelf

Answer 6

Alright thank you so much @littleelf and @peachpi !

So the z-score for Al's Orchards would be 1.56 and for Zippy's Orchards it would be -0.69. Therefore the rotten apple was more likely to come from Zippy's Orchards because -0.69 is closer to the mean than 1.56. Correct?

Answer 7

yes I think that's right