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In: Statistics and Probability

The pH level of soil can be very important toward plant growth, especially for blueberries which...

The pH level of soil can be very important toward plant growth, especially for blueberries which require acidic soil. Suppose the population distribution of soil pH levels in our area is normally distributed with a population mean pH level of 5.5 and a population standard deviation of 0.1.

  1. a.) Suppose you select a random sample of size n=1 from your backyard and test the soil. What is the probability of selecting soil with a pH less than 5.46?

  2. b.) Suppose instead you select a random sample of size n=25 from your backyard and calculate an average pH from this larger sample. Find the mean and standard deviation of the sampling distribution for ??̅

  3. c.) Given the sample in part c, (n=25), what is the probability of selecting soil with an average pH less than 5.46?

  4. d.) Why is there a difference between the answer to part a and part d?

  5. e.) Based on the Empirical Rule, (68-95-99.7), 95% of the sample mean pH levels for samples of size n=25 should fall between what two pH levels?

  6. f.) What pH level represents the 95 percentile of sample means for samples of size n=25?

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Expert Solution

orchestra answered 3 years ago
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