In April 2025
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Americans ate an average of
25.7 pounds of confectionery products each last year
and spent an average of $61.50 per person doing so. If
the standard deviation for consumption is 3.75 pounds
and the standard deviation for the amount spent is
$5.89, find the following:
a. The probability that the sample mean confectionary
consumption for a random sample of 40 American
consumers was greater than 27 pounds
b. The probability that for a random sample of 50, the
sample mean for confectionary spending exceeded
$60.00
The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 7. Find the probability that more than four road construction projects are currently taking place in the city
In a dental surgery conducted by a country dental health team, 500 adults were asked to
give the reason for their last visit to a dentist. Of the 220 who had less than a high-school
education or better, 150 stated that they went for preventative reasons. Construct a 95
percent confidence interval.
Student scores on a test that measures self-image are approximately normally distributed. This test is administered to 20 science students and the mean and standard deviation of their test scores are 88 and 24, respectively.
a) Find a 98% confidence interval of the true mean.
b) What can we assert with 98% confidence about the possible size of our error if we estimate the mean score to be 88?
The lifespan of rats raised in a laboratory is approximately normally distributed with a standard deviation of 5.9 months. A sample of 31 rats reared to adulthood in a laboratory have a mean lifespan of 27.3 months.
a) Find a 95% confidence interval for the population mean of all rats raised in a laboratory.
b) What can we assert with 95% confidence about the possible size of our error if we estimate the mean lifespan of all laboratory rats to be 27.3 months?
c) How large a sample is needed if we wish to be 95% confident that our sample mean will be within 3.5 months of the true mean?
A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calorie content is approximately normal.
The yield of a chemical process is being studied. From a previous experience yield is known to be normally distributed and σ = 3. The past 5 days if plant operation have to resulted in the following percent yields: 91.6,88.75,90.8,89.95, and 91.3. Find a 95% two-sided confidence interval on the true mean yield.
A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calorie content is approximately normal.
A confidence interval estimate is desired for the gain in a circuit on a semiconductor device. Assume the gain is normally distributed with standard deviation σ = 20.
a) Find a 95% confidence interval for μ when n = 10 and x̄ = 1000.
b) Find a 95% confidence interval for μ when n = 25 and x̄ = 1000.
c) Find a 99% confidence interval for μ when n = 10 and x̄ = 1000.
d) Find a 99% confidence interval for μ when n = 25 and x̄ = 1000.
The width and height of the normal curve distribution is determined by the
