Let us assume that the weights of the polar bear are normally distributed. Let x be a random variable representing the weights. We would calculate the z score by applying the formula,
[tex]z\text{ = }\frac{x\text{ - }\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]
where
x = sample mean
μ = population mean
σ = population standard deviation
n = sample size
From the information given,
x = 1100
μ = 990
σ = 95
n = 7
Thus,
[tex]z\text{ = }\frac{1100\text{ - 990}}{\frac{95}{\sqrt[]{7}}}\text{ = 3.06}[/tex]We want to find P(x > 1100). This can be rewritten as
P(x > 1100) = 1 - P(x ≤ 1100)
To find P(x ≤ 1100), we would find the probability value corresponding to the z score of 3.06 from the normal distribution table. Thus,
P(x ≤ 1100) = 0.99889
P(x > 1100) = 1 - 0.99889
P(x > 1100) = 0.00111
the probability that the mean weight of 7 Polar Bears would be over 1100 pounds is 0.00111
