Question

The diameters of ball bearings are distributed normally. The mean diameter is 104 millimeters and the standard deviation is 3 millimeters. Find the probability that the diameter of a selected bearing is greater than 109 millimeters. Round your answer to four decimal places.

Answer 1

Answer: The probability that the diameter of a selected bearing is greater than 109 millimeters is 0.047

Step-by-step explanation:

Since the diameters of ball bearings are distributed normally, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = the diameters of ball bearings.

µ = mean diameter

σ = standard deviation

From the information given,

µ = 104 millimeters

σ = 3 millimeters

The probability that the diameter of a selected bearing is greater than 109 millimeters is expressed as

P(x > 109) = 1 - P(x ≤ 109)

For x = 109,

z = (109 - 104)/3 = 1.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.953

Therefore,

P(x > 109) = 1 - 0.953 = 0.047