A normal population has a mean of 21 and a standard deviation of 5.
Compute the z value associated with 24
What proportion of the population is between 21 and 24?
What proportion of the population is less than 18?
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To compute the z-value associated with a given value, you can use the formula:
z = (x - μ) / σ
where:
- x is the given value (24 in this case),
- μ is the mean of the population (21 in this case), and
- σ is the standard deviation of the population (5 in this case).
Substituting the values into the formula:
z = (24 - 21) / 5
z = 3 / 5
z = 0.6
The z-value associated with 24 is 0.6.
To determine the proportion of the population between 21 and 24, we need to find the area under the curve between these two values on a standardized normal distribution table, or by using statistical software.
The proportion of the population less than 18 can also be determined similarly.
To find these proportions using a standardized normal distribution table:
1. Locate the z-score corresponding to each value (21, 24, and 18) in the table.
2. Find the corresponding area/proportion in the table for each z-score.
3. Calculate the desired proportions by subtracting the smaller area from the larger area.
Alternatively, you can also use statistical software or tools to calculate these proportions effortlessly.