Using the normal distribution, it is found that the mean is of and the standard deviation is of .
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, we have that the p-value of Z when X = 30 is of 0.1, hence, when X = 30, Z = -1.28, so:
The p-value of Z when X = 32.5 is of 0.2, hence when X = 32.5, Z = -0.84, hence:
Hence:
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-5x = - 7 because -6x plus x is -5x and use elimination to get rid of the -3y so you end up with -5x = -7
Answer:
Correct option is (A).
Step-by-step explanation:
Let <em>p</em> = proportion of water samples that exceeded the desired pH level.
A sample of size <em>n</em> = 648 is selected. Of these samples <em>X</em> = 62 exceeded the desired pH levels.
The confidence interval for the population proportion is given by:
The MOE or margin of error is estimated difference between the true population parameter value and the sample statistic value.
The information provided is:
MOE = 0.02
Compute the 90% confidence interval for the proportion of water samples that exceeds the desired pH level as follows:
Thus, the 90% confidence interval for the proportion of water samples that exceeds the desired pH level is (8%, 12%).
This confidence interval implies that there is a 90% confidence that the river water exceeds the desired pH level between 8% and 12% of the time studied.
The correct option is (A).