Question

a researcher is studying a group of field mice. the distribution of the weight of field mice is approximately normal with mean 25 grams and standard deviation 4 grams. which of the following is closest to the proportion of field mice with a weight greater than 33 grams?

Answer 1

The proportion of field mice weighing more than 33 grams in the distribution will be about 0.2275

• Mean, μ = 25 grams
• Standard deviation, σ = 4 grams
• Score, X = 33 grams

We need to calculate the P(Z > Zscore)

Recall :

Zscore = (X - μ) ÷ σ

For X > 33 :

Zscore = (33 - 25) ÷ 4 = 2

Therefore, the probability would be expressed as :

P(Z > 2) = 1 - P(Z < 2)

From the normal distribution table :

P(Z < 2) = 0.97725

Therefore,

P(Z > 2) = 1 - 0.97725 = 0.02275

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