Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean = 57.0 kg and standard deviation = 8.0 kg. Suppose a doe that weighs less than 48 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)

______________

(b) If the park has about 2500 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)

____________

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 50 does should be more than 54 kg. If the average weight is less than 54 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x

for a random sample of 50 does is less than 54 kg (assuming a healthy population)? (Round your answer to four decimal places.)

_______________

(d) Compute the probability that x

< 58.7 kg for 50 does (assume a healthy population). (Round your answer to four decimal places.)

____________________

Suppose park rangers captured, weighed, and released 50 does in December, and the average weight was x

= 58.7 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

Since the sample average is above the mean, it is quite likely that the doe population is undernourished.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished.

Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.

_______________________________________

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. Suppose a small group of 16 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.32 gram.(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

lower limit________

upper limit ________

margin of error_____________

(b) What conditions are necessary for your calculations? (Select all that apply.)

is known

normal distribution of weights

is unknown

n is large

uniform distribution of weights

(c) Interpret your results in the context of this problem.

There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.09 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

_______________ hummingbirds

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Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken six blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with = 1.89 mg/dl.(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.)

lower limit________ upper limit __________ margin of error _________

(b) What conditions are necessary for your calculations? (Select all that apply.)

uniform distribution of uric acid

n is large

is unknown

is known

normal distribution of uric acid

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average uric acid level for this patient is 0.95.

The probability that this interval contains the true average uric acid level for this patient is 0.05.

There is not enough information to make an interpretation.

There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.

There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.10 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)

_____________blood tests

________________________________________

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 42 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that is known to be $1.96 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

lower limit $_________

upper limit $________

margin of error $________________

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.29 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)

_______________farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

lower limit $_________

upper limit $__________

margin of error $_______________