June 2022 p51 q5
3173
The lengths, in cm, of the leaves of a particular type are modelled by the distribution \(N(5.2, 1.5^2)\).
Find the probability that a randomly chosen leaf of this type has length less than 6 cm.
Solution
The lengths are normally distributed with mean \(\mu = 5.2\) and standard deviation \(\sigma = 1.5\).
We need to find \(P(X < 6)\).
Standardize the variable: \(Z = \frac{X - \mu}{\sigma}\).
Substitute the values: \(Z = \frac{6 - 5.2}{1.5} = 0.5333\).
Find \(P(Z < 0.5333)\) using standard normal distribution tables or a calculator.
The probability is approximately 0.703.
Log in to record attempts.