Answer:
- <u><em>4,099 units or more</em></u>
Explanation:
The cumulative distribution of a random variable X that follows a normal distribution is given by the area undear the "bell curve" and the values are given by the corresponding table for the standard normal distribution.
The standardized value of the variable X is called Z and is calculated with the formula:
Where:
You read the Z-value for which the probability is greater than or equal to 5% in the table for the values of the area to the right of Z. Using probability = area under the curve ≥ 5%, the Z-value is 1.645 (interpolating between p = 0.0495, Z = 1.64 and p = 0.0505, Z = 1.65).
Substituting in the formula for Z:
- 1.645 = (X - 4,000) / 60
- X= 60 × 1.645 + 4,000 = 4,098.7 ≈ 4,099
Hence, the bonus will be paid on 4,099 units or more.