Question

The mean length of a pine needle is 3.2 inches with standard deviation of .148 inches. What's the probability that a random sample of 44 needles has a mean over 3.5 inches

Answer 1

0.02133

Explanation:

We solve using the z score formula

z = (x-μ)/σ

where

x is the raw score = 3.5

μ is the population mean = 3.2

σ is the population standard deviation =0.148 inches

For x > 3.5

z = 3.5 - 3.2/0.148

z = 2.02703

Probability value from Z-Table:

P(x<3.5) = 0.97867

P(x>3.5) = 1 - P(x<3.5)

P(x>3.5) = 1 - 0.97867

P(x>3.5)= 0.02133

The probability that a random sample of 44 needles has a mean over 3.5 inches is 0.02133