Question

A biologist found that Polar Bears have a mean weight of 990 pounds with standard deviation of 95 pounds.Find the probability that the mean weight of 7 Polar Bears would be over 1100 pounds.

Answer 1

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,

`z\text{ = }\frac{x\text{ - }\mu}{\frac{\sigma}{\sqrt[]{n}}}`

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,

`z\text{ = }\frac{1100\text{ - 990}}{\frac{95}{\sqrt[]{7}}}\text{ = 3.06}`

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