The scores on a psychology exam were normally distributed with a mean of $67$ and a standard deviation of $8$. A failing grade on the exam was anything $2$ or more standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed?

The scores on a psychology exam were normally distributed with a mean of $67$ and a standard deviation of $8$. What is the standard score for an exam score of $55?$

Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

The weights of babies born at Belmont Hospital are normally distributed with a mean of $6.8$ pounds and a standard deviation of $1.2$ pounds.

The body mass indexes of American men between the ages of $30$ and $50$ are normally distributed with a mean of $26.2$ and a standard deviation of $4.7$. a. Determine the standard score and the percentile of a BMI of $25$. b. Determine the standard score and the percentile of a BMI of $28$. c. Several health organizations have declared that men with a BMI of $25$ or greater are overweight and that men with a BMI of $30$ or greater are obese. What percentage of American men are overweight? Obese?

State, with an explanation, whether you would expect the following data set to be normally distributed. Scores awarded a large class on an easy economics exam

The scores on a psychology exam were normally distributed with a mean of $67$ and a standard deviation of $8$. About what percentage of scores were less than $59?$

Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

If you want to reduce the margin of error in your pre-election survey, you should use a larger sample.

Actual lengths of pregnancy terms are nearly normally distributed about a mean pregnancy length (of about $38$ to $39$ weeks) with a standard deviation of $15$ days.

About what percentage of births would be expected to occur more than $15$ days after the mean pregnancy length?

The scores on a psychology exam were normally distributed with a mean of $67$ and a standard deviation of $8$.

If $500$ students took the exam, approximately how many students scored below $75$?

The scores on a psychology exam were normally distributed with a mean of $67$ and a standard deviation of $8$. What is the standard score for an exam score of $79?$

Determine whether the following study described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls. In a study of the effects of magnets on back pain, some subjects were treated with magnets while others were given nonmagnetic devices with a similar appearance (Journal of the American Medical Association). (The magnets did not appear to be effective in treating back pain.)

For the given exam grades, briefly describe the shape and variation of the distribution.

Exam results for $100$ students: median $=82$, mean $=65$, low score $= 22$, high score $=100$

The resting heart rates for a sample of individuals are normally distributed with a mean of $70$ and a standard deviation of $15$. Use the $68$-$95$-$99.7$ rule to find out the percentage of heart rates in each of the following categories. a. greater than $85$ b. less than $40$ c. less than $85$ d. less than $100$ e. greater than $70$ f. less than $55$ g. greater than $40$ h. between $55$ and $100$

Determine whether the following variable is qualitative or quantitative, and explain why. The breeds of all cats at an animal rescue shelter