Question
Gabriela Garcia, a researcher at Honduras Coffee Corporation, is interested in determining the rate of coffee use per household in Honduras. She believes that annual household consumption has a normal distribution with a mean of 12 pounds and a standard deviation of 3.25 pounds. If Gabriela takes a sample of 20 households, what is the probability that Honduran households consume more than 13.5 pounds of coffee annually on average? Write your answer using 4 decimal places.
97
likes484 views
Answer to a math question Gabriela Garcia, a researcher at Honduras Coffee Corporation, is interested in determining the rate of coffee use per household in Honduras. She believes that annual household consumption has a normal distribution with a mean of 12 pounds and a standard deviation of 3.25 pounds. If Gabriela takes a sample of 20 households, what is the probability that Honduran households consume more than 13.5 pounds of coffee annually on average? Write your answer using 4 decimal places.
Corbin
4.6108 Answers
1. **Identify given information:**
- Mean (\(\mu\)):12
- Standard deviation (\(\sigma\)):3.25
- Sample size (\(n\)):20
- Sample mean (\(\bar{X}\)):13.5
2. **Calculate the standard error of the mean (SEM):**
\text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{3.25}{\sqrt{20}} = \frac{3.25}{4.4721} \approx 0.7274
3. **Convert the sample mean to a z-score:**
z = \frac{\bar{X} - \mu}{\text{SEM}} = \frac{13.5 - 12}{0.7274} \approx \frac{1.5}{0.7274} \approx 2.0623
4. **Find the probability (P) corresponding to the z-score (using Z-tables or a calculator):**
P(Z > 2.0623) = 1 - P(Z \leq 2.0623) \approx 1 - 0.9806 = 0.0194
Therefore, the probability that the average coffee consumption is more than 13.5 pounds is approximatelyP(\bar{X} > 13.5) \approx 0.0194
- Mean (\(\mu\)):
- Standard deviation (\(\sigma\)):
- Sample size (\(n\)):
- Sample mean (\(\bar{X}\)):
2. **Calculate the standard error of the mean (SEM):**
3. **Convert the sample mean to a z-score:**
4. **Find the probability (P) corresponding to the z-score (using Z-tables or a calculator):**
Therefore, the probability that the average coffee consumption is more than 13.5 pounds is approximately
Frequently asked questions (FAQs)
How many kilometers are in 100 miles then convert the answer to meters?
+
Math question: What is the measure (in degrees) of an angle at the center of a circle with a circumference of 40cm?
+
What is the average number of pets owned by the students in a class if 25% have no pets, 50% have 1 pet, and 25% have 2 pets?
+
New questions in Mathematics