Question

The weights of adult male birds of a certain species are normally distributed with a mean of 27.5 grams and a standard deviation of 1.1 grams. What is the z-score of a male bird of this species with a weight of 29.37 grams?

Answer 1

The z-score of a male bird of this species with a weight of 29.37 grams is 1.7.

Explanation:

We are given that the weights of adult male birds of a certain species are normally distributed with a mean of 27.5 grams and a standard deviation of 1.1 grams.

Let X = weights of adult male birds of a certain species

So, X ~ Normal(
`\mu=27.5,\sigma^(2) =1.1^(2)`)

The z score probability distribution for normal distribution is given by;

Z =
`( X-\mu)/(\sigma ) }` ~ N(0,1)

where,
`\mu` = population mean weight = 27.5 grams

`\sigma` = standard deviation = 1.1 grams

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

SO, the z-score of a male bird of this species with a weight of 29.37 grams is given by;

Z score =
`( X-\mu)/(\sigma ) }` =
`( 29.37-27.5)/(1.1 ) }`

= 1.7