P(X >65)= P| H 65 – 50 10 = P(z>1.5) =1-P(z<1.5) [U sin g the excel function =1-0.9332 =NORM.DIST(1.5,0,1,TRUE) = 0.067
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
I understand how you guy got 1.5 but after 1.5 how did you get 0.9332 and then the answer 0.067 can you break this problem down for me
![### Solving Probability Using the Standard Normal Distribution
To calculate the probability \( P(X > 65) \) for a normally distributed variable \( X \) with a mean (\(\mu\)) of 50 and a standard deviation (\(\sigma\)) of 10, follow these steps:
1. **Standardize the Variable**:
Convert \( X \) to a standard normal variable \( z \) using the formula:
\[
P(X > 65) = P\left( \frac{X - \mu}{\sigma} > \frac{65 - 50}{10} \right)
\]
Substituting the values, we get:
\[
P(X > 65) = P(z > 1.5)
\]
2. **Find the Complementary Probability**:
To use standard normal distribution tables or functions, it's often easier to find the cumulative probability up to a point and subtract from 1:
\[
P(z > 1.5) = 1 - P(z < 1.5)
\]
3. **Use Standard Normal Distribution Table or Function**:
The cumulative probability \( P(z < 1.5) \) can be found using a standard normal distribution table or a computational tool such as Excel:
\[
1 - P(z < 1.5) \approx 1 - 0.9332
\]
This step involves using the Excel function:
\[
\text{Using the Excel function: } \text{=NORM.DIST}(1.5, 0, 1, \text{TRUE})
\]
Here, \( NORM.DIST(1.5, 0, 1, TRUE) \) yields approximately 0.9332.
4. **Calculate the Final Probability**:
\[
P(z > 1.5) = 1 - 0.9332 = 0.067
\]
Therefore, the probability that \( X \) is greater than 65 is approximately \( 0.067 \).
This approach utilizes the properties of the standard normal distribution to simplify the problem and allows for the efficient calculation using statistical software.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16fe8730-7443-4574-bfb2-fbae5c49fbdc%2F842ebc57-c966-46f6-aa2b-807232ba7ed5%2Fhy6ti1_processed.png&w=3840&q=75)
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