An adult female of a certain breed of dog has a mean height of 33 cm and a standard deviation of 2.1 cm. What is the probability that a randomly-selected adult female of this breed has a height greater than 36.3 cm?
To find the probability that a randomly-selected adult female of this breed has a height greater than 36.3 cm, we first need to calculate the z-score for this height using the formula:
z = (X - μ) / σ
where:
X = 36.3 cm
μ = 33 cm
σ = 2.1 cm
z = (36.3 - 33) / 2.1
z = 3.3 / 2.1
z = 1.5714
Next, we look up the z-score in a standard normal distribution table or use a calculator to find the proportion of values greater than z. From the table, we find that the proportion is approximately 0.0594.
Therefore, the probability that a randomly-selected adult female of this breed has a height greater than 36.3 cm is 0.0594 or 5.94%.