the weights of a certain dog breed are approximately normally distributed with a mean of 53 pounds, and a standard deviation of 6.2 pounds. use your graphing calculator to answer the following questions. write your answers in percent form. round your answers to the nearest tenth of a percent. a) find the percentage of dogs of this breed that weigh less than 53 pounds. % b) find the percentage of dogs of this breed that weigh less than 46 pounds. % c) find the percentage of dogs of this breed that weigh more than 46 pounds. %

The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values of the set tend to be near to the mean (also known as the expected value), whereas a high standard deviation shows that the values are spread out over a larger range.

Solution:

Mean weight (μ) = 53 pounds

Standard deviation (σ) = 6.2 pounds

The z-score for any given weight, 'X', is given by the following expression;

z = (X - μ)/σ

(i) P(X<53)

Since 53 pounds is exactly the mean weight, 50% of the dogs weight more than 53 pounds while 50% weight less than 53 pounds.

P(X<53) = 50.0%

(ii) P(X<46)

z = (46-53)/6.2

z = -1.12

this is equivalent to 15.2 percentile

P(X<46) = 15.2%

(iii) P(X>46)

P(X>46) = 100% - P(X<46) = 100% - 15.2%

P(X>46) = 84.8%

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