Answer :
The Probability can be obtained as approximately 0.9992 or 99.92%.
To find the probability that a single randomly selected value from a normal distribution falls within a certain range, we can use the standard normal distribution table or a calculator.
In this case, we want to find the probability that a randomly selected value from the population with μ = 97.9 and σ = 15.9 falls within a certain range.
We need to convert this problem to a standard normal distribution by calculating the z-score for the given value and using the z-table or calculator to find the corresponding probability.
To calculate the z-score, we use the formula: z = (x - μ) / σ
Substituting the given values: z = (150 - 97.9) / 15.9 = 3.26 (approx.)
Using a z-table or calculator, we can find the probability that a randomly selected value from the standard normal distribution is less than 3.26.
This probability represents the area under the curve to the left of the z-score.
The probability can be obtained as approximately 0.9992 or 99.92%.
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The probable question may be:
A population of values has a normal distribution with \( \mu=97.9 \) and \( \sigma=15.9 \). If a random sample of size \( n=20 \) is selected a. Find the probability that a single randomly selected value from a normal distribution falls within a certain range.
