Exam 5: The Standard Deviation As a Ruler and the Normal Model

The systolic blood pressure of $\text { 18-year-old }$ women is normally distributed with a mean of $120 \mathrm {~mm } \mathrm {~Hg }$ and a standard deviation of $12 \mathrm {~mm} \mathrm {~Hg } .$ Draw and label the Normal model for systolic blood pressure.What percentage of $\text { 18-year-old }$ women have a systolic blood pressure between $96 \mathrm {~mm} \mathrm {~Hg }$ and $144 \mathrm {~mm} \mathrm {~Hg? }$

σ = 20,48% above 150; μ = ?

μ = 30,37% below 20; σ = ?

The free throw percentages for the participants of a basketball tournament were compiled.The percents ranged from 40% to 96% with a mean of 53% and a standard deviation of 8%.The quartiles and median percentages were 50%,84%,and 53%.This year's tournament percentages are 3% higher than last year's tournament percentages.Find last year's tournament mean,median,and standard deviation of the free throw percentages.

0.7 < z < 1.98

What should a Normal Probability plot look like for normally distributed data?

the highest 7%

Suppose that the average amount of sugar a person eats per year is 7 kg with a standard deviation of 1.5 kg.How many standard deviations from the mean is the consumption of 11 kg of sugar?

The weights of children age two average 24 pounds with a standard deviation of 2 pounds.How many standard deviations from the mean is a weight of 17 pounds?

On a recent English exam,if 20% of scores fell below 60 points and the standard deviation is 7.5,find the mean score (assuming the Normal model is appropriate).

Based on the Normal model for car speeds (in km/h)on a road N(77,9.1),what is the cutoff value for the lowest 30% of the speeds?

A town's average snowfall is 40 cm per year with a standard deviation of 5 cm.According to the Normal model,what percent of snowfall is less than 3 standard deviations from the mean?

Here are the summary statistics for the monthly payroll for an accounting firm: $\text { lowest salary } = \$ 60,000 \text {, }$ $\text { mean salary } = \$ 140,000 \text {, }$ median = $100,000,range = $240,000, IQR = $120,000, $\text { first quartile } = \$ 70,000$ standard deviation = $80,000. Suppose that business has been good and the company gives every employee a $\$ 10,000$ raise.Give the new value of each of the summary statistics.

The mean test score on a statistics test was 72 with a standard deviation of 10.How many standard deviations from the mean is a test score of 90?

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by $\mathrm { N } ( 42,8 )$ Draw and label the Normal model.Then find the interval for the middle 95% of snowfall.

The local basketball team averages 65% from the free throw line.A player who makes 72.5% of his free throws has a z-score of 1.5.Find the standard deviation.

The scores for a recent English exam can be represented by the Normal model N(67,6.3).What score would you expect to be unusually low for this exam?

You heard that the average number of years of experience among stockbrokers is 14 years.You can't remember the standard deviation somebody with 8 years' experience has a z-score of -2.Find the standard deviation.

An English instructor gave a final exam and found a mean score of 70 points and a standard deviation of 5.1 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Then find the percent of scores above 85.3 points.

On an exam Bob scored 75% and was 1.5 standard deviations above the mean of 63%.What was the standard deviation?