The results of a certain medical test are normally distributed with a mean of 130 and a standard deviation of 12. (A reading above 149 is considered unhealthy.) Use the given table to find the percentage of people with readings above 141.
To find the percentage of people with readings above 141, we will use the standard normal distribution table (also known as the Z-table).
Step 1: Standardize the value of 141 using the formula:
Z = (X - μ) / σ
where:
Z is the standardized value,
X is the observed value,
μ is the mean, and
σ is the standard deviation.
In this case, X = 141, μ = 130, and σ = 12. Plugging in these values, we get:
Z = (141 - 130) / 12 = 11/12 ≈ 0.92
Step 2: Look up the corresponding area in the standard normal distribution table for the Z-value obtained in Step 1. The table gives you the area to the left of the Z-value.
In this case, the Z-value is approximately 0.92. Looking up this value in the standard normal distribution table, we find that the area to the left of 0.92 is approximately 0.8212.
Step 3: Calculate the area to the right of the Z-value by subtracting the area to the left of the Z-value from 1.
In this case, the area to the right of 0.92 is:
1 - 0.8212 = 0.1788 (or 17.88% when expressed as a percentage).
Therefore, the percentage of people with readings above 141 is approximately 17.88%.
Note: The standard normal distribution table may not include the exact Z-value. In such cases, you can use interpolation to estimate the corresponding area.
To find the percentage of people with readings above 141, we need to calculate the z-score and then use the standard normal distribution table.
The z-score formula is given by:
z = (x - μ) / σ
where:
x is the individual value,
μ is the mean, and
σ is the standard deviation.
In this case, the individual value is 141, the mean is 130, and the standard deviation is 12.
Substituting the values into the formula:
z = (141 - 130) / 12
z = 11 / 12
z = 0.917
Now we can use the standard normal distribution table to find the percentage of people with readings above 141.
Looking up the z-score of 0.917 in the table, we find that the percentage corresponding to this z-score is approximately 0.8183.
Therefore, the percentage of people with readings above 141 is approximately 81.83%.