Question

Suppose that the weights of 2700 registered female Great Danes in the United States are

distributed normally with a mean of 133 lb. and a standard deviation of 6.4 lb.
Approximately how many of the Great Danes weigh less than 126.6 lbs.? SHOW WORK!

Answer 1

To solve this problem, we can use the cumulative distribution function (CDF) of the normal distribution.Given:

Mean (μ) = 133 lb

Standard Deviation (σ) = 6.4 lb

Weight (X) = 126.6 lb

We can use the formula for the standard normal distribution to calculate the z-score:

z = (X - μ) / σ

Plugging in the values, we get:z = (126.6 - 133) / 6.4 = -0.984375

Now, we can use a standard normal distribution table or a calculator with a built-in normal distribution function to find the cumulative probability (P) associated with the z-score of -0.984375.

Using a standard normal distribution table, we find that the cumulative probability for a z-score of -0.984375 is approximately 0.1611.

So, approximately 16.11% of the registered female Great Danes in the United States weigh less than 126.6 lbs.

Explanation: