Final answer:
To find the probability of randomly selecting an individual pill that weighs less than 540mg and 560mg, we need to consider the distribution of weights and use the z-score formula. This formula compares the weight of the pill to the mean and standard deviation of the distribution, allowing us to calculate the probability using a z-table or a calculator.
Step-by-step explanation:
To find the probability of randomly selecting an individual pill that weighs less than 540mg and 560mg, we need to consider the distribution of weights. If we assume that the weights of the pills are normally distributed, we can use the z-score formula to calculate the probability. The z-score formula is given by:
z = (x - μ) / σ
where x is the weight of the pill, μ is the mean weight, and σ is the standard deviation.
- First, find the z-score for 540mg: z1 = (540 - μ) / σ
- Next, find the z-score for 560mg: z2 = (560 - μ) / σ
- Calculate the cumulative probability for z1 and z2 using a z-table or a calculator.
- Subtract the cumulative probability of z1 from the cumulative probability of z2 to find the probability of randomly selecting a pill with a weight between 540mg and 560mg.