8. Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 30% of these tanks leak. You randomly choose 30 tanks at random. (a) Does the binomial setting apply? Explain. (b) What is the mean number of leaking tanks in such samples of 30 tanks? What is the standard deviation? (c) What is the probability that exactly 25 of these tanks leak? (d) What is the probability that at most 15 tanks leak in samples of 30 tanks?
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
#8
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 alt="**7. Lamb’s-quarter Analysis**
Lamb’s-quarter is a weed that affects corn growth. A study involved planting corn with fixed numbers of Lamb’s-quarter plants. The data below show weeds per meter and yield:
| | Mean | SD |
|-------------------|-------|-------|
| Weeds per meter | 3.25 | 3.61 |
| Yield | 162.9125 | 8.66 |
With a correlation of -0.457, answer these:
(a) **Equation of Regression Line:** Determine using variables.
(b) **Slope Interpretation:** Explain slope in context of the problem.
(c) **Intercept Interpretation:** Discuss significance of y-intercept in context.
(d) **Variation Explanation:** Proportion of yield variation explained by regression.
**8. Leakage from Gasoline Tanks**
30% of underground tanks leak. You choose 30 tanks randomly.
(a) **Binomial Setting:** Criteria and explanation.
(b) **Mean and Standard Deviation:** Calculate for leaking tanks in sample.
(c) **Probability of 25 Tanks Leaking:** Determine exact probability.
(d) **Probability of at Most 15 Tanks Leaking:** Calculate probability.
**9. Wechsler Adult Intelligence Scale (WAIS)**
WAIS scores for adults are normally distributed (mean 100, SD 15).
(a) **95th Percentile Score:** Determine.
(b) **Sampling Distribution for SRS of 60:** Describe.
(c) **Probability of Average Score ≥ 105:** Calculate for SRS of 60.
**10. Student Poll on New Sports Team**
A SRS of 104 students, 37 oppose new sports team. Find and interpret a 90% confidence interval for proportion not in favor.
**11. Final Exam Grade Analysis**
Grades for 8:00 am final exam:
| | 100 | 98 | 95 | 91.5 | 104.5 | 94 | 86 | 84.5 | 73 | 92.5 |
|-------|-----|-----|----|------|-------|----|----|------|----|------|
| 86.5 | 73.5 | 87 | 72.5 | 82 | 68.5 | 64.5 | 90.75 | 66.5 |
Check for outliers.
**12. Redwood Tree Diameter Study**
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