Question

1. The weights of a certain dog breed are approximately normally distributed with a mean of ? = 46 pounds, and a standard deviation of ? = 7 pounds.

A) A dog of this breed weighs 51 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed. z =

B) A dog has a z-score of -0.8. What is the dog's weight? Round your answer to the nearest tenth as needed. ____ pounds

C) A dog has a z-score of 0.8. What is the dog's weight? Round your answer to the nearest tenth as needed. _____ pounds

2. For a standard normal distribution, find:

P(z > c) = 0.4953

Find c.

3) About _____ % of the area under the curve of the standard normal distribution is outside the interval z=[?2.52,2.52]z=[-2.52,2.52] (or beyond 2.52 standard deviations of the mean).

Answer 1

Let X be the dog's weight

X ~N(46, 7)

A) When X = 51 , The Z score is  

B) When Z = -0.8

The dog's weight is

Answer: 40.4 pounds

C) When Z -score = 0.8, the dog's weight is

Answer: 51.6 pounds

Q 2)

Therefore From Normal table, c = 0.0119

Answer: C = 0.0119

Q 3) The Area under the curve

P(-2.52<Z< 2.52) = P(-2.52<Z<0)+P(0<Z<2.52) = 0.4941+0.4941 =0.9882

Therefore the area outside the curve is =1 - 0.9882 =0.0118

Hence, 1.18% of the area under the curve of the standard normal distribution is outside the interval z=[?2.52,2.52]