Thank you for visiting A population of values has a normal distribution with tex mu 97 7 tex and tex sigma 96 2 tex You intend to draw a. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The probability that a single randomly selected value from the population is between 85.5 and 122.1 is approximately 0.4638.
To find the probability that a single randomly selected value is between 85.5 and 122.1, we can calculate the z-scores corresponding to these values and then use the standard normal distribution table or a statistical software to find the area under the curve between these z-scores.
First, we calculate the z-scores for 85.5 and 122.1 using the formula: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
For 85.5:
z1 = (85.5 - 97.7) / 96.2 = -0.127
For 122.1:
z2 = (122.1 - 97.7) / 96.2 = 0.253
Next, we use the standard normal distribution table or a statistical software to find the area between these z-scores. The area represents the probability of a single randomly selected value falling between 85.5 and 122.1.
Using the standard normal distribution table or a statistical software, we find that the area between z1 = -0.127 and z2 = 0.253 is approximately 0.4638.
Therefore, the probability that a single randomly selected value is between 85.5 and 122.1 is approximately 0.4638.
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