water in the east basin. 7.1-6. To determine whether the bacteria count was lower in the west basin of Lake Macatawa than in the east basin, n = 37 samples of water were taken from the west basin and the number of bacteria colonies in 100 milliliters of water was counted. The sample characteris- tics were = 11.95 and s = 11.80, measured in hundreds of colonies. Find an approximate 95% confidence interval for the mean number of colonies (say, µ w) in 100 milliliters of water in the west basin. %3D 7.1-7. Thirteen tong
water in the east basin. 7.1-6. To determine whether the bacteria count was lower in the west basin of Lake Macatawa than in the east basin, n = 37 samples of water were taken from the west basin and the number of bacteria colonies in 100 milliliters of water was counted. The sample characteris- tics were = 11.95 and s = 11.80, measured in hundreds of colonies. Find an approximate 95% confidence interval for the mean number of colonies (say, µ w) in 100 milliliters of water in the west basin. %3D 7.1-7. Thirteen tong
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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7.1-6

Transcribed Image Text:**Transcription for Educational Website:**
**Topic: Bacteria Count in Lake Macatawa**
1. **Background Information:**
- This section investigates the bacteria count in the east and west basins of Lake Macatawa.
- Samples of water were collected to count bacteria colonies in 100 milliliters of water.
2. **East Basin Sampling:**
- A total of \( n = 30 \) samples of water were taken.
- The number of bacteria colonies, measured in hundreds, in each 100 milliliters of water from the east basin are as follows:
- 93, 140, 8, 120, 3, 120, 33, 14, 94, 98, 100, 23, 110, 57, 76, 9, 73, 53, 28, 49, 66, 9, 73, 70, 27, 91, 53, 37, 92, 53.
3. **West Basin Sampling:**
- A total of \( n = 37 \) samples of water were taken.
- Sample characteristics:
- Mean (\( \bar{x} \)) = 11.95
- Standard Deviation (\( s \)) = 11.80
- Measured number of colonies in hundreds.
- An approximate 95% confidence interval is constructed for the mean number of colonies (\( \mu \)) in 100 milliliters of water in the west basin.
4. **Confidence Interval Calculation:**
- An approximate 90% confidence interval for the mean number of colonies (\( \mu_{E} \)) in the east basin is required.
5. **Example of Other Items:**
- A random sample of \( n = 6 \) wheels of cheese yielded weights (in pounds) as follows:
- 22.90, 22.00, 18.55, 19.40, 18.95, 21.50, 22.35.
**Analysis & Reporting:**
- The data set provides insights into the potential differences in bacteria counts between the east and west basins of Lake Macatawa.
- The use of statistics, such as mean, standard deviation, and confidence intervals, helps in understanding the variation and reliability of the bacterial presence in the water
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