exam 3

Uniform distribution

100

What shape is a uniform distribution?

A rectangle / straight lines

200

What is the formula for finding x for a uniform distribution?

f(x) = (b-a) x (1/d-c)

a & b = represent the area you're trying to find

c & d = represent the full range of the distribution

300

The time it takes to get called back at one doctor's office follows a uniform distribution between 10 and 25 minutes. The doctor's office guarantees patients that it will take no longer than 20 minutes for them to get called back. For what percent of patients does it take longer than that?

.33 / 33%

(use basic fractions after drawing)

400

The time it takes to get called back at one doctor's office follows a uniform distribution between 10 and 25 minutes. The doctor's office guarantees patients that it will take no longer than 20 minutes for them to get called back, and if it does they'll receive a 50% discount on their appointment. If they want to give a discount to no more than 3% of their patients, what should their guaranteed time limit be?

24.55 minutes

draw, label unknown value as a, use area formula to find a

500

A tool-and-die machine shop produces extremely high-tolerance spindles. The spindles are 18-inch slender rods used in a variety of military equipment. A piece of equipment used in the manufacture of the spindles malfunctions on occasion and places a single gouge somewhere on the spindle. However, if the spindle can be cut so that it has 14 consecutive inches without a gouge, then the spindle can be salvaged for other purposes. Assuming the location of the gouge alongside the spindle is uniformly distributed, What's the probability that a defective spindle can be salvaged?

.44

(4(1/18) + 4(1/18)

Normal distribution

100

What shape is a normal distribution?

Bell curve / symmetrical mound

200

What are the formulas for normal distributions and what are they used for?

1. Normalcdf (for finding a probability)

2. Invnorm (for finding an a value)

300

Men’s weights are normally distributed with a mean of 𝜇 = 182.9 lbs and a standard deviation of 𝜎 = 40.8 lbs. Find the probability that a randomly selected man will weigh between 170 and 180 lbs.

.0957 / 9.57%

400

Women's heights are normally distributed with a mean of 64.1 inches and a standard deviation of 2.5 inches. What percentage of women can fight through a 72 inch door?

.9992

500

Women's heights are normally distributed with a mean of 64.1 inches and a standard deviation of 2.5 inches. Out of 150,000,000 women in the USA, how many would be over 6 ft tall?

120,000 women (find percentage taller than 6 ft then multiply it to be 150,000,000)

Exponential distribution

100

What shape is an exponential distribution?

A curved diagonal line

200

If the mean of an exponential distribution is 3, what is the standard deviation?

3

300

What are the formulas for exponential distributions and when do we use them?

p (x>a) = e^{-a / theta}

p (x<a) = 1 - e^{-a / theta}

400

The lifetime of a new brand of light bulbs follows an exponential distribution with a mean of 2500 hours of use. Find the probability that a randomly selected light bulb lasts less than 3125 hours?

.71

(1-e^-a/theta)

500

The time between arrivals at an ATM machine follows an exponential distribution with a mean of 10 minutes. Find the probability that at least 15 but no more than 25 minutes pass between arrivals.

.141

.223 - .082

Sampling distribution

100

What shape are sampling distributions?

Normal

200

How do you find the mean and standard deviation of sampling distributions?

The sample mean & the sample standard deviation divided by the square root of n

300

Men’s weights are normally distributed with a mean of 𝜇 = 182.9 lbs and a standard deviation of 𝜎 = 40.8 lbs. For a sample of 36 men, find the mean and standard deviation of the sampling distribution.

Mean: 182.9

Standard deviation: 6.8

400

Explain to me what the Central Limit Theorem means as if teaching a lecture.

The sampling distribution as explained by the central limit theorem states that within a population, the means of many samples with a size of 30 or more will create a normal distribution.

500

Women have heart rates that are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. The lowest 3% of women's heart rates are below ___ and the top 3% are above ___

55.7 and 99.3

(invNorm)

Confidence interval

100

Explain to me what a confidence interval is.

an estimate of target parameters

200

How do you find a confidence interval in your calculator.

stat, tests, 7, standard deviation / mean / n / c-level

300

A population has a mean of 71.6 and a standard deviation of 4.6. A sample within this population has 36 people. Find a confidence interval of 95% confidence to represent this population.

(70.097, 73.103)