Answer:
0.02133
Step-by-step 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
