Statistics

Central Limit Theorem

100

The average GPA at a particular school is 2.89 with a standard deviation .63. A random sample of 25 students is collected. Find the standard error of your sample.

Standard error is ơ(ẍ)= ơ/√n =.63/√25 =.126

200

According to a recent study, the average age that an american adult leaves home is 26 years old. Assume that this variable is nomally distrubuted with a standard deviation of 2.4 years. If a random sample of 20 adults is selected, find the probability that the mean age the participants left home is greater than 25 years old to the nearest tenth.

standard error=.537, Z=-1.86, 96.9%

300

The average number of tornadoes in Kansas is 47 per year, with a standard deviation of approximately 14.2 tornadoes. If a random sample of 15 years is selected, find the probability that the mean number of tormadoes is less than 50 to the nearest tenth.

79.3%

400

A set of SAT scores are normally distributed with a mean of 1518 and a standard devuiation of 325. Find the probability that if a sample of 100 scores were selected, their mean would be less than 1500.

29.1%. (Ref ES pg 296)

500

Based on data from the National Health and Nutrition Examinations Survey, assume that weights of men are normally distributed with a mean of 172lb and a standard deviation of 29lb. Find the probability that 20 randomly selected men will have a mean weight that is greater than 180lbs.

What is 10.9%. (ref ES 296)

Z scores Maybe

100

A set of 5000 scores on a college readiness exam are known to be normally distributed with a mean of 72 and standard deviation of 6. To the nearest integer value, how many scores are there between 63 and 75?

N=5000, µ=72, ơ = 6 Find the corresponding z values for x=63 and x=75. We get z=-1.5 and .5 62% of scores fall in the range .62*5000= approx. 3123 scores

200

A manufacturer of TV sets found that for the sets he produces, the lengths of time until the first repair can be described using a normal model with a mean of 4.5 years and a standard deviation of 1.5 years. If the manufacturer sets the warrantee so that only 10.2% of the 1st repairs are covered by the warrantee, how long should the warrantee last?

Find the zvalue that corresponds to p=.102 z=-1.27 Z=(x-µ)/ơ x=2.595 so approx. 2.6 years

300

Based on data from the National Health and Nutrition Examinations Survey, assume that weights of men are normally distributed with a mean of 172lb and a standard deviation of 29lb. Find the probability that a man will be greater than 180lbs.

38.97% or 39%

400

The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72". Heights of men are normally distributed with a mean of 69.0" and a standard deviation of 2.8". If a male passenger is randomly selected, find the probabity that he can fit through the doorway without bending rounded to the nearest tenth.

85.8%

500

Suppose a consumer advocacy group would like to conduct a survey to find the proportion p of consumers who bought the newest generation of an MP3 player were happy with their purchase. a) How large a sample n should they take to estimate p with 2% margin of error and 90% confidence?

Extra prob. #5

Pot Luck

100

The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72". Heights of men are normally distributed with a mean of 69.0" and a standard deviation of 2.8". If half of the passengers are men, find the probability that the mean height of the 100 men is less than 72".

99.99%

200

For women aged 18-24, systolic blood pressures are normally distibuted with a mean of 114.8 and a standard devitaion of 13.1. Hypertension is commonly definded as a systolic blood pressure above 140. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 140.

2.7%

300

For women aged 18-24, systolic blood pressures are normally distibuted with a mean of 114.8 and a standard devitaion of 13.1. Hypertension is commonly definded as a systolic blood pressure above 140. If 4 women in this age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.

.01%

400

The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72". Heights of men are normally distributed with a mean of 69.0" and a standard deviation of 2.8". What doorway height would allow 95% of men of enter the aircraft without bending?

73.6" or greater

500

The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72". Heights of men are normally distributed with a mean of 69.0" and a standard deviation of 2.8". What doorway height satisfies the condition that there is a 95% probability that this height is greater than the mean height of 100 men?

69.5"

Confidence Levels

100

What is the formula for finding the Confidence interval?

CL=x +/- E

200

A measure that describes a characteristic of a population, such as the mean or standard deviation, is called a?

parameter.

300

A fire truck manufacturer has determined based on a sample of 80 trucks, that one model of truck will allow fire fighters to spray a stream of water an average of 40 yards. The standard deviation of the measure is thought to be 6 yards. Use a 95% confidence interal to find the maximum error of estimate of the distance water can be sprayed.

1.3 yards

400

A company gives four-hour boat tours for a dolpin watch. On 30 tours, the time between first leaving the dock to sighting a dolphin averaged 125 minutes. Assume a normal distribution with a standard deviation of 28 minutes. Find a 95% confidence interval for the mean time until the first dophin sighting of all tours.

115

500

A city manager is preparing a report on recycling efforts. She finds the daily total weight of recycled material for 30 randomly selected days of the year. These weights are nomally distrubuted with an average weight of 22,500 pounds and a standard deviation of 11,100 pounds. Find a 90% confidence interval for the one-day mean weight of recycled material.

19,166

Functions

100

Solada's net pay is 65% of her gross pay, and she budgets $600 per month for living expenses. She estimates that she can save 20% of her remaining money, so her one-month savings f(x) for a gross pay of x dollars is given by f(x)0 0.2(0.65x-600). Find the inverse function.

100x/13 + 12,000/13

200

What is the domain and range for: sqrt(x-7) +3

Domian x> or equal to 7, Range is y= or greater than 3.

300

What shape will this function look like? f(x)= -x^2+3x-5

upside down U

400

Solada's net pay is 65% of her gross pay, and she budgets $600 per month for living expenses. She estimates that she can save 20% of her remaining money, so her one-month savings f(x) for a gross pay of x dollars is given by f(x)0 0.2(0.65x-600). What restrictions, if any, should be put on the domains of the function and its inverse?

x> or equal to 923.08.

500

Solada's net pay is 65% of her gross pay, and she budgets $600 per month for living expenses. She estimates that she can save 20% of her remaining money, so her one-month savings f(x) for a gross pay of x dollars is given by f(x)0 0.2(0.65x-600). Determine Solada's gross pay for one month if her savings for that month were $120.

$1846.15