Posted: November 3rd, 2015

Statistics

Statistics

1.An adult has on average 5.2 liters of blood.  Assume the variable is normally distributed and has a standard deviation of 0.3.  Find the percentage of people who have less than 5.4 liters of blood in their system.  Draw the curve and shade the region.

2.  The average monthly mortgage payment in the US is $982.  If and the variable is normally distributed, find the following probabilities for a randomly selected monthly payment

At least $1000 (Draw the curve and shade the region)

No more than $950 (Draw the curve and shade the region)

Between $800 and $1150 (Draw the curve and shade the region)

To qualify for a police academy, candidates must score in the top 10% on a general abilities test.  Assume test scores are normally distributed with a mean of 200 and a standard deviation of 20.  Find the lowest possible score to qualify.  Draw the curve and shade the region.

An automobile dealer finds that the average price of a used car is $8500.  She decides to sell cars that appeal to the middle 70% of the market in terms of price.  Find the minimum and maximum prices of the cars the dealer will sell.  The standard deviation is $1150, and the variable is normally distributed.  Draw the curve and shade the region.

The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year.  If the benefits are normally distributed with a standard deviation of $425, find the probability that the mean benefit for a random sample of 36 patients is less than $3800.  Draw the curve and shade the region.

The growing seasons for a random sample of 35 U.S. cities were recorded, yielding a sample mean of 190.7 days with a population standard deviation of 54.2 days.  Estimate for all U.S. cities the true mean of the growing season with 95% confidence.  Round to the nearest tenth.

Interval used (z or t):_________________________        Interval:_________________________

A large department store found that it averages 362 customers per hour.  Assume that the standard deviation is 29.6 and a random sample of 40 hours was used to determine the average.  Find the 99% confidence interval of the population mean.

Interval used (z or t):_________________________        Interval:_________________________

A scientist wishes to estimate the average depth of a river.  How many sample measurements should be taken if he wants to be 99% confident that the estimate is accurate to within 2 feet?  A previous study determined the standard deviation to be 4.33 feet.   Use the formula

The data represent a random sample of the number of home fires started by candles for the past several years.  Find the 90% confidence interval for the true mean number of fires started by candles each year.

5460          5900           6090          6310          7160            8440         9930

Interval used (z or t):_________________________        Interval:_________________________

A sample of 14 randomly selected commuters showed the average of the commuting times was 33.2 minutes.  If the standard deviation was 8.3 minutes, find the 95% confidence interval for the population mean.

Interval used (z or t):_________________________        Interval:_________________________

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