Question - Probability Calculations for Normal Distribution with Sample Size of 100
Solution:
The image contains four separate parts (a through d) of a question regarding a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 4. It then asks about the probabilities related to a sample (n) of 100. Here are the answers to each of the parts as provided in the image:a. What is the probability that X is less than 49?The answer is given as P(X < 49) = 0.0062.b. What is the probability that X is between 49 and 50.5?The answer is given as P(49 < X < 50.5) = 0.8822.c. What is the probability that X is above 50.6?The answer is given as P(X > 50.6) = 0.0688.d. There is a 40% chance that X is above what value?The answer is given as X = 50.1012.The calculations for these probabilities would typically involve using the standard normal distribution (Z-distribution), where you would standardize the values using the formula $$ Z = \frac{X - μ}{σ} $$. Since the sample size is 100, the standard error of the mean (SEM) would also be involved, computed by $$ SEM = \frac{σ}{\sqrt{n}} $$. However, the full workings of these calculations are not shown in the image; it only provides the final numerical results. If you need further assistance on how to perform these calculations, please feel free to ask!
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