IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What percentage of people have an IQ score less than 117, to the nearest tenth?
Using a standard normal distribution table or calculator, we can find the z-score corresponding to an IQ score of 117:
z = (117 - 100) / 15 = 1.13
Looking at the standard normal distribution table, we can find that the area to the left of z = 1.13 is 0.8708. This means that approximately 87.08% of people have an IQ score less than 117. Rounded to the nearest tenth, this is 87.1%. Therefore, about 87.1% of people have an IQ score less than 117.
For males in a certain town, the systolic blood pressure is normally distributed with a mean of 125 and a standard deviation of 5. What percentage of males in the town that have a systolic blood pressure higher than 131, to the nearest tenth?
Using a standard normal distribution table or calculator, we can find the z-score corresponding to a systolic blood pressure of 131:
z = (131 - 125) / 5 = 1.2
Looking at the standard normal distribution table, we can find the area to the right of z = 1.2 is 0.1151. This means that approximately 11.51% of males in the town have a systolic blood pressure higher than 131. Rounded to the nearest tenth, this is 11.5%. Therefore, about 11.5% of males in the town have a systolic blood pressure higher than 131.
To find the percentage of people with an IQ score less than 117, we can use the concept of standard deviation and the z-score.
The z-score is calculated by subtracting the mean from the given value and then dividing by the standard deviation.
Let's calculate the z-score for an IQ score of 117:
z = (117 - 100) / 15
= 17 / 15
= 1.13
Next, we need to find the area under the standard normal distribution curve to the left of the z-score of 1.13. Using a standard normal distribution table, we can find the corresponding percentage.
Looking up the z-score of 1.13 in the table, the area to the left is approximately 0.8708.
So approximately 87.1% of people have an IQ score less than 117.
Therefore, the percentage is 87.1% (rounded to the nearest tenth).