Respuesta :
Answer:
A) 8
Step-by-step explanation:
Mean weight = u = 25 pounds
Standard Deviation = [tex]\sigma[/tex] = 4 pounds
We have to find how many beagles out of 75 will weigh more than 30. Since the data is normally distributed, we can use z score to find this value. First we will what is the percentage(probability) of a randomly selected beagle to weigh more than x = 30 pounds, using this percentage we can then find our answer.
The formula for z score is:
[tex]z=\frac{x-u}{\sigma}[/tex]
Using the values, we get:
[tex]z=\frac{30-25}{4}=1.25[/tex]
So, P(Weight > 30) is equivalent to P(z > 1.25). Using the z table, we can write:
P(z > 1.25) = P(Weight > 30) = 0.1056
This, 0.1056 or 10.56% of the beagles are expected to weigh more than 30 pounds.
So,out of 75 beagles, 10.56% of 75 are expected to weigh more than 30 pounds.
10.56% of 75 = 0.1056 x 75 = 7.92 = 8 (rounding to nearest integer)
Therefore, out of 75 beagles 8 are expected to weigh more than 30 pounds.
The number of people expected to weigh more than 30 pounds is; 8 pounds
How to calculate normal distribution?
We are given;
Mean; μ = 25 pounds
Standard deviation; σ = 4 pounds
Sample size; n = 75
sample mean; x' = 30
Formula for z-score is;
z = (x' - μ)/σ
z = (30 - 25)/4
z = 1.25
From online p-value from z-score calculator, we have;
p-value = 0.1056
Thus, number of people expected to weigh more than 30 pounds is;
Number of people = 0.1056 * 75 = 7.92 approximately 8 people
Read more about normal distribution at; https://brainly.com/question/4079902
