Cumulative Probability DistributionsThe regulatory authority selects a random tablet from Batch Z2. Based on previous knowledge, you know that Batch Z2 has a mean paracetamol level of 510 mg, and its standard deviation is 20 mg.What is the probability that the tablet that has been selected by the authority has a paracetamol level below 550 mg?
Question
Cumulative Probability DistributionsThe regulatory authority selects a random tablet from Batch Z2. Based on previous knowledge, you know that Batch Z2 has a mean paracetamol level of 510 mg, and its standard deviation is 20 mg.What is the probability that the tablet that has been selected by the authority has a paracetamol level below 550 mg?
Solution
To solve this problem, we need to use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.
Step 1: Calculate the Z-score. The formula for the Z-score is:
Z = (X - μ) / σ
where: X = value in the dataset (in this case, 550 mg) μ = mean of the dataset (in this case, 510 mg) σ = standard deviation of the dataset (in this case, 20 mg)
So, Z = (550 - 510) / 20 = 2
Step 2: Look up the Z-score in the Z-table. The Z-table tells us what percentage of the population is below (to the left of) our score.
Looking up a Z-score of 2 in the Z-table gives us a value of 0.9772. This means that 97.72% of the tablets have a paracetamol level below 550 mg.
So, the probability that the tablet selected by the authority has a paracetamol level below 550 mg is 0.9772 or 97.72%.
Similar Questions
Continuous Probability DistributionsNow, the company’s QC (Quality Control) department comes and selects a tablet at random from Batch Z2. It is interested in finding if the paracetamol level is above 450 mg or not.What is the probability that the tablet selected by QC has a paracetamol level above 450 mg?
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