Question

In a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation is 5.5 days. One length of gestation had a z-score of –1.70. Which of the following sentences best interprets this z-score?
The length of this gestation period was longer than the mean length of gestation periods by 1.7 days.
The length of this gestation period was shorter than the mean length of gestation periods by 1.7 days.
The length of this gestation period was longer than the mean length of gestation periods by 1.7 standard deviations.
The length of this gestation period was shorter than the mean length of gestation periods by 1.7 standard deviations.

Answer 1

Answer:

The length of this gestation period was shorter than the mean length of gestation periods by 1.7 standard deviations.

Step-by-step explanation:

Mathematically, to obtain the z-score, we use the following formula;

z-score = (x-mean)/SD

The z-score obtained can either be positive or negative. When z-score obtained is positive, it shows that the given value is bigger than the mean. In cases where z-score is negative, it means that the value we are calculating is smaller than the mean.

In the given formula, the value x represents the value which we are comparing against the mean value.