**For 20 points**

- A state school administrator claims that the standard deviation of test scores for 8th grade students who took a life-science assessment test is at most 35. You work for the administrator and you are asked to test this claim. You find that a random sample of size 36 tests that you collected has a standard deviation of 37.6. At α = 0.1, do you have enough evidence to support the administrator’s claim? Assume test scores are normally distributed.
__Please show all 5 steps involved__

**For 15 points**

- In a simple random sample of 30 luxury cars, the sample average annual fuel cost was $5425 and a sample standard deviation of $807.55. Construct the 90% confidence interval for the population mean. Assume that the annual fuel cost is normally distributed. Please interpret your result.
__Please show all work__ **15 points)**

The reading speed of sixth-grade students is approximately normal, with a mean of 138 words per minute and a standard deviation of 27 words per minutes.

- What is the probability that a randomly selected sixth-grade student reads more than 118 word per minute?

- What is the probability that a randomly selected sixth-grade student reads less than 140 words per minute?

- What is the probability that a randomly selected sixth-grade student will read between 118 words and 168 words per minute?

- What is the reading speed of a sixth-grade student that separate the lower 80% to the rest of sixth grade students?

- What reading
**speeds**separate the middle 74% of reading speed of sixth-grade students to the rest?

**For 20 points**

**For 20 points**

- According to a survey conducted by the vegetarian Digest, it has been claimed that less than 78% of American adults eat salad once or more times per week. Christian Frederic, a reputable trainer and nutritionist, is disputing the claim by the vegetarian Digest. He conducted a survey of 275 adults in America and finds that 205 of them eat salad once or more times per week. Conduct the appropriate test addressing the nutritionist’s suspicions. Use a 0.01 level of significance.
__Please show all 5 steps involved__

**For 15 points**

- You wish to estimate, with a 74% confidence, the population proportion of Metaluna Adults who think they have a comfortable saving account. Your estimate must be accurate within 4.6% of the population proportion.
- No preliminary estimate is available. Find the minimum sample size needed.

- Find the minimum sample size needed, using a prior estimate that found that 33.33% of U.S adults think that they have a comfortable saving account.

**For 15 points**

- You randomly select and weigh 23 samples of an allergy medication. The sample standard deviation is 1.23 milligrams. Assuming the weights are normally distributed, construct 80% confidence intervals for the population variance and standard deviation. Please interpret your result.
__Please show all work__

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