Question

A species of snakes studied in a certain area in South America has some exceptionally large individuals, for some reason yet unknown to scientists. The weights of the studied population are strongly right‑skewed with mean 36 kg and standard deviation 7 kg. A random sample of 75 snakes is taken.

What is the probability that the mean weight of the sample is greater than 37 kg?

cannot say

0.1075

0

0.4432

Answer 1

Solution:

X: follows the right skewed distribution. Here the sample size = n = 75

As per central limit theoerem,

a population with mean μ and standard deviation σ and take sufficiently large random samples from the population, then the distribution of the sample means will be approximately normally distributed.

Therefore,

μ=36, σ=7, n=75

We have to find

Using z-score,

Therefore,

P(Z>1.2372) = 1 - P(Z<1.2372)

P(Z>1.2372) = 1-0.8920 ...Using z table

P(Z>1.2372) = 0.1080

Hence, the probability that the mean weight of the sample is greater than 37 kg is 0.1080

Done