The mean weight of a litter of puppies is 7.1 pounds, with a standard deviation of 1.2 pounds. Carly wants to know the weight of the puppy she is buying, but the seller only has the z-score of −0.25. How much does the puppy weigh?

6.8 pounds
7.4 pounds
5.9 pounds
8.3 pounds
7.3 pounds

6.8 pounds

Step-by-step explanation:

Assuming the weight of a litter of puppies is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = weight of a liter of puppies.

µ = mean weight

σ = standard deviation

From the information given,

µ = 7.1 pounds

σ = 1.2 pounds

the seller only has the z-score of −0.25, looking at the probability distribution table, the z score corresponding to the 0.25 is

- 0.68

Therefore,

- 0.25 = (x - 7.1)/1.2

Cross multiplying by 1.2, it becomes

- 0.25 × 1.2 = x - 7.1

- 0.3 = x - 7.1

x = - 0.3 + 7.1

x = 6.8

A. 6.8 is correct

Step-by-step explanation:

a z-score is found by using the formula x=(x-u)/o where z is the z-score, x is the puppy's weight in this case, u is the mean, and o is the standard deviation

-0.25=(x-7.1)/1.2

multiply both sides by 1.2

-0.3=x-7.1

add 7.1 to both sides

6.8=x

This is how we got 6.8! Hope this helps :)

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