A normal population has a mean of 22 and a standard deviation of 5. 1. Compute the z value associated with 25.
2. What proportion of the population is between 22 and 25?
3. What proportion of the population is less than 18?

Given Information:

Mean = μ = 22

Standard deviation = σ = 5

Required Information:

1. z-value = ?

2. P(22 < X < 25) = ?

3. P(X < 18) = ?

1. z-value = 0.6

2. P(22 < X < 25) = 22.58%

3. P(X < 18) = 21.19%

Step-by-step explanation:

What is Normal Distribution?

Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability

1. We want to find out the z-value associated with 25

Therefore, the z-value associated with X = 25 is 0.6

2. We want to find out the proportion of the population that is between 22 and 25.

The z-score corresponding to 0 is 0.50

The z-score corresponding to 0.6 is 0.7258

Therefore, the proportion of the population that is between 22 and 25 is 22.58%

3. We want to find out the proportion of the population that is less than 18

The z-score corresponding to -0.8 is 0.2119

Therefore, the proportion of the population that is less than 18 is 21.19%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.0, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.6 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

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step-by-step explanation: