Chapter 6 (S2)

The precision scientific company manufactures thermometers that are supposed to give readings of 0° C at the freezing point of water, some thermometers give readings below 0° C (denoted by negative numbers) and some give readings above 0° (denoted by positive numbers) . Assuming the same parameters as above, what is the probability that a randomly selected thermometer

.9332-.0228 = .9104

In standard normal distribution, the mean is ___ and the standard deviation is ____. While in normal distribution it is not.

0; 1

For samples of size n larger than ___, the distribution of the sample means can be approximated reasonably well by normal distribution.

30

Continuity correction x = fewer than 8 (doesn't include 8)

7.5 and below

Continuity correction x = at least 8 Includes 8 and above)

7.5 is the lower

When you have no upper x, use ____

8

Continuity correction x = more than 8 (doesn't include 8)

8.5 is the lower

Continuity correction x = at most 8 (includes 8 and below)

8.5 is the upper

The precision scientific company manufactures thermometers that are supposed to give readings of 0° C at the freezing point of water, some thermometers give readings below 0° C (denoted by negative numbers) and some give readings above 0° (denoted by positive numbers) . Assuming the same parameters as above, what is the probability of selecting a thermometer that shows the freezing point of the water as above -1.23?

P(z > -1.23) = 1 - (P(z < -1.23) = 1 - .1093 = .8907

Probability that the number of job applicants late for interviews is between 5 and 9 inclusive

The area between 4.5 and 9.5

Probability of no more than 15 peas with green pods

The area to the left of 15.5

The distribution of sample x will, as the sample size increases, approach _________.

a normal distribution

z with a fish shape next to it means

a z score with its area to the right

P(a < z < b) denotes the probability that the z score is

between a and b

z-score

distance along horizontal scale of the standard normal distribution; refer to the leftmost column and top row of A-2

Binomial distributions

fixed number trials, each trial independent, trials classified as success or failure

Binomial Distribution Calculator?

go to normalcdf and use it

P(z >) denotes the probability that the z score is

greater than a

continuity correction

it is made to a discrete whole number x in the binomial distribution by representing the discrete whole number x by interval form

When you have table with pages for negative and positive z-scores, the values in the body of the table are the cumulative area from the ____ yp to a vertical boundary above a specific z-score

left

areas (or probabilities) are positive or zero values, but they are never _________

negative

If the original population is ______ _______, then for any sample size n, the sample means will be normally distributed (not just for values of n larger than 30)

normally distributed

Are probability, area, and percentile the same?

yes

How to convert the values of normal distributions into z scores?

z = (data (x) - mean (μ))/standard deviation

difference between a z-score and area

z scores are distances along the horizonatal scale but areas are regions under the normal curve

the standard deviation of sample means is s, the mean of sample means is

μ

Find z0.02

1 - .02 = .98 which is 2.05

The precision scientific company manufactures thermometers that are supposed to give readings of 0° C at the freezing point of water, some thermometers give readings below 0° C (denoted by negative numbers) and some give readings above 0° (denoted by positive numbers) . If one thermometer is randomly selected, find the probability that, at the freezing point of water, the reading is less than 1.27°

89,80% or 0.898

-1.2

Find the area of the shaded region. The graph depict IQ scores of adults, those are normally distributed with a mean of 100 and a standard deviation of 15

.5747

Find the area of the shaded region. The graph depict IQ scores of adults, those are normally distributed with a mean of 100 and a standard deviation of 15

Locate .6 on the z vertical, then find the .05 on the horizontal, the number between them (.7422) is the answer

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

We will take the one closest to the positive end and subtract it from the one on the negative end for the answer, .843 - .2358 = .6285

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

z = (70 -100)/15 = -2

Find the indicated IQ score. The graphs depict IQ scores of adults and those are normally distributed with a mean of 100 and a standard deviation of 15.

-.62

Find the indicated z-score

-1.53

Find the indicated z-score

Assume the population of weights of men is normally distributed with a mean of 172 ib and a standard deviation of 29 ib. Find the probability that 20 randomly selected men will have a mean weight that is greater than 175 in (so that their total weight exceeds the safe capacity of 3500 ib)

First find the new standard deviation, s = σ/(square root of n); s = 29/square root of 20, s = 6.4845. Now use this to find the z-score 175-172/6.4895 = .4626, now put it into the calulcator for probability, make the lower .4626 and the upper -10. The probability os .3228

Determine if certain size requirements are met to use the normal distribution. The probability that at least 92 people recognize McDonald's brand name, the probability of a random person doing so is 95%

So we need to see if np _> 5 and the nq _> 5, (100)(.95) = 95_>5 so yes, (100)(.05) = 5, so yes

The part of the z-score denoting hundredths is found _____ of the table

across the top

central limit theorem

for a population with ANY distribution, the distribution of the sample means approaches a normal distribution as the sample size increases. The procedure in this section form the foundation for estimating population parameters and hyposis testing.

What conditions must be satisfied to make the probabilities from a binomial probability distribution approximated well by using a normal distribution with a mean μ = np, and a standard deviation σ = √(npq)?

if the np _> 5 and the nq _> 5

P(z < a) denotes the probability that the z score is

less than a

a z score must be ____ whenever it is located on the left half of the normal distribution

negative

q

probability of failure in one of the n trials

p

probability of success in one of the n trials

are

region under the curve; refer to the values in the body of Table A-2

x

the exact number of successes, within n trials

n

the fixed number of trials

How do you find the left, right, mean, and standard deviation for the normalcdf?

the left and right can be found by x-0.5 and x + 0.5.

round z-scores to ____ decimal places

two

Continuity correction x = exactly 8

upper is 8.5, lower is 7.5

What formula to use to find irregular z-scores

z = (x -μ)/α

How do you find the standard deviation (s) for all central means?

σ/(square root of n), n is the sample size