Estimating Mean and Standard Deviation

A local bank charges a $20 service fee per month and pays out 2% interest. These transactions happen consecutively on the same day. Typically, the bank applies the interest first and then takes out the $20 service fee. The mean bank account balance before these successive transactions is $4,200 with a standard deviation of $125. What is the new mean balance after these transactions?

• $4,264

• $4,200

• $4,184

• $4,100

Mr. White’s test scores for a very easy test are calculated and found to have an average of 87 with a standard deviation of 6 points. He then realizes he mistakenly added 10 points for an extra credit assignment to all the test scores instead of a homework assignment. When he takes those 10 points off (boo) what will the new mean and standard deviation of the test scores be?

• Mean: 77, Standard Deviation: 6

• Mean: 87, Standard Deviation: 6

• Mean: 77, Standard Deviation: 0

• Mean: 87, Standard Deviation: 0

The city’s radar detectors are malfunctioning. They have been over estimating the speeds of cars by 3 mph. (Measured speeds = Actual speeds + 3). If the city has been measuring cars speed and found the mean to be 72 mph with a standard deviation of 4 mph, what can they expect the new values to be after the speeds are adjusted?

• Mean: 69 mph, Standard Deviation: 4 mph

• Mean: 72 mph, Standard Deviation: 4 mph

• Mean: 75 mph, Standard Deviation: 4 mph

• Mean: 69 mph, Standard Deviation: 7 mph

The number of grains of coffee found in a brewed espresso has a mean of 12 grains with a standard deviation of 2 grains. Quality control is trying out new filters that claim to reduce the number of grains allowed through by half. They also claim that using filtered water can decrease the number of grains that make it through the filter by three on average. The equation for this transformation is $ y = 0.5x - 3 $. What is the mean and standard deviation for the number of grains in the drink if both new measures are used?

• Mean: 3 grains, Standard Deviation: 1 grain

• Mean: 6 grains, Standard Deviation: 1 grain

• Mean: 3 grains, Standard Deviation: 2 grains

• Mean: 6 grains, Standard Deviation: 2 grains

In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?

• Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day

• Approximately normal with mean 5.5 days and standard deviation 2.6 days

• Approximately normal with mean 5.5 days and standard deviation 0.26 day

A biologist wants to estimate the difference between the mean body lengths of green and brown stinkbugs. A random sample of 20 green stinkbugs has a mean body length of 16.22 millimeters (mm) and a standard deviation of 1.34 mm. A random sample of 20 brown stinkbugs has a mean body length of 13.41 mm and a standard deviation of 0.73 mm. What is the standard error of the difference (green - brown) between the sample means?

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Employees at a large company can earn monthly bonuses. The distribution of monthly bonuses earned by all employees last year has mean 2.3 and standard deviation 1.3. Let z represent the standard normal distribution. If x represents the mean number of monthly bonuses earned last year for a random sample of 40 employees, which of the following calculations will give the approximate probability that x is less than 2 ?

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Let X be a random variable that has a skewed distribution with mean µ = 10 and standard deviation σ = 10. Based on random samples of size 400, the sampling distribution of X is

• highly skewed with mean 10 and standard deviation 10

• highly skewed with mean 10 and standard deviation 5

• highly skewed with mean 10 and standard deviation 0.5

• approximately normal with mean 10 and standard deviation 10

• approximately normal with mean 10 and standard deviation 0.5

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

• Approximately normal with mean $206,274 and standard deviation $3,788

• Approximately normal with mean $206,274 and standard deviation $37,881

• Approximately normal with mean $206,274 and standard deviation $520

• Strongly right-skewed with mean $206,274 and standard deviation $3,788

• Strongly right-skewed with mean $206,274 and standard deviation $37,881

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

• 0.1151

• 0.2743

• 0.7257

• 0.8849

• Based on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated.