Answer:
the probability of that the sample mean will have 12year or larger is 0.4013, .
Step-by-step explanation:
The probability that a sample mean is 12 or larger for a sample from the horse population is:
Given,
N, number of sample =60 horses
x₁, variate mean= 12 years.
x, mean age = 10 years.
σ, standard deviation = 8 years.
To calculate for the probability, we are going to use the formula of normal distribution.
normal distribution is calculated by:
z=[
x₁−x]/ σ
where z is called the normal standard variate,
x₁ is the value of the variable,
x is the mean value of the distribution and
σ is the standard deviation of the distribution.
The z-value corresponding to 12year is
z=[
x₁−x]/ σ
z=[12
−10]/ 8 =2/8=0.25
we will use the table of normal distribution to find the corresponding z value.
From Table of z, the area corresponding to a z-value of 0.25 is 0.0987.
The total area under the standardized normal curve is unity and since the curve is symmetrical,
The area to the right of the z=0.25 ordinate is 0.5000−0.0987= 0.4013.
Thus, the probability of the sample mean is 0.4013, for 60 horses, it is likely that 60 * 0.4013 =24.08 = 24 horses will have 12year or larger.
