The probability that the sample's mean length is greater than 4.8 inches is 0.6554
What is the probability the sample's mean length is greater than 4.8 inches?
To find the required probability, we need to calculate the z-score of 4.8 inches and then use the standard normal table to find the corresponding probability.
The z-score is calculated as follows:
z = (x - μ) / σ
Where:
- Sample mean, x = 4.8
- Population mean, μ = 5
- Population standard deviation, σ = 0.5
Substitute the known values into the equation
z = (4.8 inches - 5 inches) / 0.5 inches
z = -0.4
Using the standard normal table, we have
P(z > -0.4) = 0.6554
So, the probability that the sample's mean length is greater than 4.8 inches is 0.6554, or 65.54%