# Statistic anlaysis Sampling Distributions

**Question description**

**1-Bass - Samples:** The bass in Clear Lake have weights that are normally distributed with a mean of 1.9 pounds and a standard deviation of 0.9 pounds.

(a) If you catch 3 random bass from Clear Lake, find the probability that the mean weight is **less** than 1.0 pound. **Round your answer to 4 decimal places. **

(b) If you catch 3 random bass from Clear Lake, find the probability that the mean weight it is **more** than 3 pounds. **Round your answer to 4 decimal places. **

**2-The bass in Clear Lake have weights that are normally distributed with a mean of 2.1 pounds and a standard deviation of 0.6 pounds.What percentage of all randomly caught groups of 3 bass should weigh between 1.9 and 2.4 pounds? **

**Enter your answer as a percentage rounded to one decimal place.**

**%**

**3-Bass - Samples:** The bass in Clear Lake have weights that are normally distributed with a mean of 2.2 pounds and a standard deviation of 0.6 pounds. Suppose you catch a*stringer* of 6 bass with a total weight of 16.5 pounds. Here we determine how *unusual* this is.

**(a) What is the mean fish weight of your catch of 6? Round your answer to 1 decimal place. pounds(b) If 6 bass are randomly selected from Clear Lake, find the probability that the mean weight is greater than the mean of those you caught. Round your answer to 4 decimal places. (c) Which statement best describes your situation?**

**4-Lifespan:**Assume the average life-span of those born in the U.S. is 78.2 years with a standard deviation of 16 years. The distribution is not normal (it is skewed left). The good people at*Live-Longer-USA*(fictitious) claim that their regiment of acorns and exercise results in longer life. So far, 45 people on this program have died and the mean age-of-death was 83.7 years.(a) Calculate the probability that a random sample of 45 people from the general population would have a mean age-of-death greater than 83.7 years. **Round your answer to 4 decimal places. **

(b) Which statement best describes the situation for those in the *Live Longer *program?

(c) Why could we use the central limit theorem here despite the parent population being skewed?

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