Problem 3) Lead concentrations in the eggshells of California condors have a mean of 1.8 ppm and a standard deviation of 0.3 ppm. The contamination levels of eggshells are classified as "low" if the lead concentration is below 1.0 ppm, “moderate" if the lead concentration falls between 1.0 ppm and 2.4 ppm, and "high" the lead concentration is above 2.4. Assuming that the lead concentrations of eggshells follows a normal distribution, answer the following questions. (Hint* The categories of Low, Moderate, and High can help you identify the boundaries of each interval. For example, the boundaries of Low are – ∞ to 1.0.) What is the percentile of an eggshell with a lead concentration of 2.3 ppm? a. 81st b. 93rd с. 86h d. 95th What lead concentration corresponds to the 79th percentile? a. 2.04 ppm b. 2.53 ppm c. 2.43 ppm d. 2.76 ppm What proportion of eggshells are predicted to fall into the "moderate" range? а. 0.76 b. 0.97 c. 0.66 d. 1.82

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### Problem 3: Lead Concentrations in Eggshells of California Condors

The lead concentrations in the eggshells of California condors have a mean of 1.8 ppm and a standard deviation of 0.3 ppm. The contamination levels of eggshells are classified as:
- **Low**: if the lead concentration is below 1.0 ppm.
- **Moderate**: if the lead concentration falls between 1.0 ppm and 2.4 ppm.
- **High**: if the lead concentration is above 2.4 ppm.

Assuming that the lead concentrations of eggshells follow a normal distribution, answer the following questions. *(Hint: The categories of Low, Moderate, and High can help you identify the boundaries of each interval. For example, the boundaries of Low are -∞ to 1.0.)*

1. **What is the percentile of an eggshell with a lead concentration of 2.3 ppm?**
   - a. 81st
   - b. 93rd
   - c. 86th
   - d. 95th

2. **What lead concentration corresponds to the 79th percentile?**
   - a. 2.04 ppm
   - b. 2.53 ppm
   - c. 2.43 ppm
   - d. 2.76 ppm

3. **What proportion of eggshells are predicted to fall into the “moderate” range?**
   - a. 0.76
   - b. 0.97
   - c. 0.66
   - d. 1.82

4. **What does it mean for two events to be independent?**
   - a. The outcome of the first event does not affect the probabilities of the outcomes for the second event.
   - b. The probability of the first event affects the probability of the second event.

5. **Which of the following is true for the binomial probability distribution?**
   - a. Each trial has possible outcomes that are randomly distributed across space and/or time.
   - b. Each trial has two possible outcomes.
   - c. Each trial is on a continuous scale.
   - d. Each variable is ordinal.

6. **The random variable Z has a standard normal distribution. What is the probability that Z is negative?**
   - a. 0.5
Transcribed Image Text:### Problem 3: Lead Concentrations in Eggshells of California Condors The lead concentrations in the eggshells of California condors have a mean of 1.8 ppm and a standard deviation of 0.3 ppm. The contamination levels of eggshells are classified as: - **Low**: if the lead concentration is below 1.0 ppm. - **Moderate**: if the lead concentration falls between 1.0 ppm and 2.4 ppm. - **High**: if the lead concentration is above 2.4 ppm. Assuming that the lead concentrations of eggshells follow a normal distribution, answer the following questions. *(Hint: The categories of Low, Moderate, and High can help you identify the boundaries of each interval. For example, the boundaries of Low are -∞ to 1.0.)* 1. **What is the percentile of an eggshell with a lead concentration of 2.3 ppm?** - a. 81st - b. 93rd - c. 86th - d. 95th 2. **What lead concentration corresponds to the 79th percentile?** - a. 2.04 ppm - b. 2.53 ppm - c. 2.43 ppm - d. 2.76 ppm 3. **What proportion of eggshells are predicted to fall into the “moderate” range?** - a. 0.76 - b. 0.97 - c. 0.66 - d. 1.82 4. **What does it mean for two events to be independent?** - a. The outcome of the first event does not affect the probabilities of the outcomes for the second event. - b. The probability of the first event affects the probability of the second event. 5. **Which of the following is true for the binomial probability distribution?** - a. Each trial has possible outcomes that are randomly distributed across space and/or time. - b. Each trial has two possible outcomes. - c. Each trial is on a continuous scale. - d. Each variable is ordinal. 6. **The random variable Z has a standard normal distribution. What is the probability that Z is negative?** - a. 0.5
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