Assume that adults have IQ scores that are normally distributed with a mean of 101.3 and a standard deviation of 17. Find the probability that a randomly selected adult has an IQ greater than 133.7. (Hint: Draw a graph.) The probability that a randomly selected adult from this group has an IQ greater than 133.7 is (Round to four decimal places as needed.)
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
review 1/2/3/4/5/6/7/8/9/10/11/12/13/14
![**Probability and Normal Distribution of IQ Scores**
Assume that adults have IQ scores that are normally distributed with a mean of 101.3 and a standard deviation of 17. Find the probability that a randomly selected adult has an IQ greater than 133.7. (Hint: Draw a graph.)
**Solution:**
To find the probability that a randomly selected adult from this group has an IQ greater than 133.7, follow these steps:
1. **Calculate the Z-score:**
The Z-score is a measure of how many standard deviations an element is from the mean. The formula to calculate the Z-score is:
\[
Z = \frac{X - \mu}{\sigma}
\]
where:
- \( X \) is the value (133.7)
- \( \mu \) is the mean (101.3)
- \( \sigma \) is the standard deviation (17)
Substituting the given values:
\[
Z = \frac{133.7 - 101.3}{17}
\]
\[
Z = \frac{32.4}{17}
\]
\[
Z \approx 1.9059
\]
2. **Find the probability for the Z-score:**
Use the standard normal distribution table (Z-table) to find the probability corresponding to the Z-score of 1.9059. The Z-table gives the probability that a value is less than the given Z-score.
The probability corresponding to \( Z = 1.9059 \) is approximately 0.9718.
3. **Calculate the desired probability:**
To find the probability that a randomly selected adult has an IQ greater than 133.7, subtract the table value from 1:
\[
P(X > 133.7) = 1 - P(X \leq 133.7)
\]
\[
P(X > 133.7) = 1 - 0.9718
\]
\[
P(X > 133.7) \approx 0.0282
\]
Therefore, the probability that a randomly selected adult from this group has an IQ greater than 133.7 is approximately **0.0282** (rounded to four decimal places).
**Graphical Representation:**
On a graph of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90efdacf-751d-4321-aeaa-af0a9a860c3a%2F74fc5653-afbb-4fda-98c3-e8b43b4a8cfb%2Fp2xs8m9_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
