Letxbe a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Thenxhas a distribution that is approximately normal with mean=58.0kgand standard deviation=7.9kg.Suppose a doe that weighs less than49kgis 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 about2500does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)

does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight ofn=55does should be more than55kg. If the average weight is less than55kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weightx

for a random sample of55does is less than55kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability thatx

<59.1kg for55does (assume a healthy population). (Round your answer to four decimal places.)

Suppose park rangers captured, weighed, and released55does in December, and the average weight wasx

=59.1kg.Do you think the doe population is undernourished or not? Explain.

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.

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

Since the sample average is above 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 of18Allen's hummingbirds has been under study in Arizona. The average weight for these birds isx= 3.15 grams.Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with=0.28gram.(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 limitupper limitmargin of error

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

is known

normal distribution of weights

nis large

uniform distribution of weights

is unknown

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

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

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

We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.

We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of errorE=0.08for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

hummingbirds

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 takenfiveblood tests for uric acid. The mean concentration wasx=5.25mg/dl.The distribution of uric acid in healthy adult males can be assumed to be normal, with=1.79mg/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 limitupper limitmargin of error

(b)

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

is known

nis large

is unknown

normal distribution of uric acid

uniform 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.

We are 5% confident that the true uric acid level for this patient falls within this interval.

We are 95% confident that the true uric acid level for this patient falls within this interval.

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

(d)

Find the sample size necessary for a 95% confidence level with maximal margin of errorE=1.20for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)

blood tests

Thirty-twosmall communities in Connecticut (population near 10,000 each) gave an average ofx=138.7reported cases of larceny per year. Assume thatis known to be41.9cases per year.

(a)

Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limitupper limitmargin of error

(b)

Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limitupper limitmargin of error

(c)

Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limitupper limitmargin of error

(d)

Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.

As the confidence level increases, the margin of error increases.

As the confidence level increases, the margin of error remains the same.

(e)

Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.

As the confidence level increases, the confidence interval increases in length.

As the confidence level increases, the confidence interval remains the same length.

How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

661021311216064

Assume that the population ofxvalues has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean weightxand sample standard deviations. (Round your answers to four decimal places.)x=

lbs=

lb

(b) Find a 75% confidence interval for the population average weightof all adult mountain lions in the specified region. (Round your answers to one decimal place.)lower limit

lbupper limit

lb