SOLUTION: in a rice mill the bags of rice has mean weight of 5.05 kg and standard deviation is 0.02 kg. if a bag is selected at random then find the probability that its weight is below 5 kg

Question 1192325: in a rice mill the bags of rice has mean weight of 5.05 kg and standard deviation is 0.02 kg. if a bag is selected at random then find the probability that its weight is below 5 kg?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
**1. Understand the Problem**
* We're given a normal distribution of rice bag weights.
* Mean weight (μ) = 5.05 kg
* Standard deviation (σ) = 0.02 kg
* We want to find the probability that a randomly selected bag weighs less than 5 kg.
**2. Calculate the Z-score**
* The Z-score tells us how many standard deviations a value is from the mean.
* Formula: Z = (X - μ) / σ
* Where:
* X is the value we're interested in (5 kg)
* μ is the mean
* σ is the standard deviation
* Calculation: Z = (5 - 5.05) / 0.02 = -0.25
**3. Find the Probability**
* We need to find the area under the standard normal distribution curve to the left of Z = -0.25.
* You can use:
* A Z-table: Look up the value corresponding to Z = -0.25 in a standard normal distribution table.
* Statistical software or calculator: Use functions like `norm.cdf()` in Python (scipy library) or similar functions in other tools.
* **Result:** The probability of a randomly selected bag weighing less than 5 kg is approximately **0.4013**.
**In summary:**
There's about a 40.13% chance that a randomly selected bag of rice from this mill will weigh less than 5 kg.

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