Exam 10: The Normal Distributions

A researcher was interested in the lengths of brook trout and obtained the following quantile-quantile plot for determining the Normality of the distribution: Based on this graph, what is the best description of the data?

The heights of adult males are approximately Normally distributed with a mean of 70 inches and a standard deviation of 3 inches. An adult male is categorized as "short" if he is less than 64 inches tall and categorized as "tall" if he is in the top 3% of adult males in terms of height. How tall does an adult male need to be to be assigned to the "tall" category?

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg. What is the minimum total body protein that the upper 25% of adult men with cirrhosis have?

Using your calculator, what is the area under the standard Normal curve corresponding to Z > -2.62?

A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught. To ensure that the smallest 8% of the brook trout get thrown back, what should the lower cut-off be?

The following Normal quantile plot displays the brain volumes of 30 autistic children: Based on this graph, what is the best description of brain volumes?

Using your calculator, what is the area under the standard Normal curve corresponding to -0.5 < Z < 1.2?

The lengths of 1-year-old girls can be described using a Normal distribution with a mean of 29 inches and a standard deviation of 1.2 inches. Using the 68-95-99.7 rule, what percent of 1-year-old girls are smaller than 27.8 inches?

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg. What is the approximate probability that a randomly selected man with liver cirrhosis has a total body protein between 9.75 and 9.85 kg?

The pH measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0.3. What is the approximate probability that the pH measurement of a randomly selected water specimen is greater than 8.2?

A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught. What proportion of these fish are larger than 86 centimeters in length?

The distribution of vitamin C amount in vitamin drops produced by a given factory is approximately Normal, with a mean of 60.0 mg and a standard deviation of 0.5 mg. What is the approximate proportion of vitamin drops containing more than 60.75 mg of vitamin C?

Serum albumin levels in adults are distributed approximately Normally with a mean of 35 g/l and a standard deviation of 5 g/l. What is the probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l?

When using your calculator to find the area under the standard Normal curve that corresponds to a particular z score < a,

The distribution of total body protein in healthy adult men is approximately Normal with mean 12.3 kg and standard deviation 0.1 kg. What is the approximate probability that a randomly selected healthy man has a total body protein greater than 12 kg?

A researcher was interested in the survival times of brook trout after their exposure to increased levels of total dissolved solids. The following quantile-quantile plot was obtained: Based on this graph, what is the best description of the data?

Serum albumin levels in adults are distributed approximately Normally with a mean of 35 g/l and a standard deviation of 5 g/l. What serum albumin level do the lower 10% of adults have?

Birth weights at a local hospital have a Normal distribution with a mean of 110 ounces and a standard deviation of 15 ounces. What is the proportion of infants with birth weights between 125 ounces and 140 ounces?

The amount of cholesterol in a person's body produced by the liver and other cells is proposed to be Normally distributed with mean 75% and standard deviation 0.5%. What is the probability that a person produces more than 76.7% of the cholesterol in his or her body?

X has a Normal distribution with mean 50 and standard deviation 8. Which of the following statements is correct?