Question 1178715: Solve each problem.
1. Your monthly electric bill has a mean of ₱120.00. what is the percentage that you will pay an amount between ₱1,380 and ₱1,740?
2.Suppose the scores in the mathematics exam are normally distributed. If the exam has a mean score of 25 and a standard deviation of 5,what is the probability that if you take the exam you will get a score higher than 30 points?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's solve each problem step-by-step:
**Problem 1: Monthly Electric Bill**
* **Understanding the Issue:**
* The mean monthly electric bill is given as ₱120.00.
* The amounts ₱1,380 and ₱1,740 are extremely far from the mean, suggesting there might be an error in the problem statement. It's highly unlikely that monthly bills would be in those amounts.
* To solve this problem, we need a standard deviation. Let's assume a standard deviation of ₱15.00.
* **Calculations:**
1. **Calculate z-scores:**
* z1 = (1380 - 120) / 15 = 1260 / 15 = 84
* z2 = (1740 - 120) / 15 = 1620 / 15 = 108
2. **Find probabilities:**
* Because the z-scores are so high, the probability of the bill being in that range is extremely close to 0.
* **Answer:**
* The probability is essentially 0.
**Problem 2: Mathematics Exam Scores**
* **Understanding the Issue:**
* The exam scores are normally distributed.
* Mean score (μ) = 25
* Standard deviation (σ) = 5
* We want to find the probability of scoring higher than 30.
* **Calculations:**
1. **Calculate the z-score:**
* z = (X - μ) / σ = (30 - 25) / 5 = 5 / 5 = 1
2. **Find the probability:**
* P(X > 30) = P(z > 1)
* Using a z-table or calculator:
* P(z < 1) ≈ 0.8413
* P(z > 1) = 1 - P(z < 1) ≈ 1 - 0.8413 = 0.1587
* **Answer:**
* The probability of scoring higher than 30 is approximately 0.1587, or 15.87%.
Answer by ikleyn(52810)  (Show Source):
You can put this solution on YOUR website! .
Solve each problem.
1. Your monthly electric bill has a mean of ₱120.00. what is the percentage that you will pay an amount between ₱1,380 and ₱1,740?
2.Suppose the scores in the mathematics exam are normally distributed.
If the exam has a mean score of 25 and a standard deviation of 5,
what is the probability that if you take the exam you will get a score higher than 30 points?
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(1) Problem in (1) is posed incorrectly/inaccurately: the standard deviation value is missed.
(2) Problem (2) in post by @CPhill is solved  .
If the score is higher than 30, it means that it is 31 or more.
So, we should calculate P(X >= 31).
It is 0.1151. the CORRECT ANSWER
For fast calculations, I used free of charge solver at this site
https://onlinestatbook.com/2/calculators/normal_dist.html
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