Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Let's solve this problem step-by-step.
### Step 1: Identify the given values
- Mean ([tex]\(\mu\)[/tex]): 82
- Standard deviation ([tex]\(\sigma\)[/tex]): 4
- Score ([tex]\(x\)[/tex]): 88
### Step 2: Calculate the z-score
The z-score formula is given by:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
Plug in the given values:
[tex]\[ z = \frac{88 - 82}{4} \][/tex]
[tex]\[ z = \frac{6}{4} \][/tex]
[tex]\[ z = 1.5 \][/tex]
So, the z-score corresponding to the score of 88 is 1.5.
### Step 3: Find the probability using the z-score
Refer to the standard normal distribution table (the chart on page 11 of the lesson). The z-score of 1.5 corresponds to a cumulative probability.
From the standard normal distribution table, a z-score of 1.5 gives us a cumulative probability of approximately 0.9332.
### Step 4: Conclusion
The probability that a randomly chosen student scores 88 or below is approximately 0.9332.
Therefore, the correct answer is:
a. .9332
### Step 1: Identify the given values
- Mean ([tex]\(\mu\)[/tex]): 82
- Standard deviation ([tex]\(\sigma\)[/tex]): 4
- Score ([tex]\(x\)[/tex]): 88
### Step 2: Calculate the z-score
The z-score formula is given by:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
Plug in the given values:
[tex]\[ z = \frac{88 - 82}{4} \][/tex]
[tex]\[ z = \frac{6}{4} \][/tex]
[tex]\[ z = 1.5 \][/tex]
So, the z-score corresponding to the score of 88 is 1.5.
### Step 3: Find the probability using the z-score
Refer to the standard normal distribution table (the chart on page 11 of the lesson). The z-score of 1.5 corresponds to a cumulative probability.
From the standard normal distribution table, a z-score of 1.5 gives us a cumulative probability of approximately 0.9332.
### Step 4: Conclusion
The probability that a randomly chosen student scores 88 or below is approximately 0.9332.
Therefore, the correct answer is:
a. .9332
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.