Stats

Difference between a standard normal distribution and a nonstandard normal distribution...

-standard normal distribution has a mean of 0, standard dev. of 1 -nonstandard normal distribution has a different value for one or both parameters

Find the area of a shaded region...

Calc: [2nd] [VARS] [normalcdf] [Enter]

Find the indicated z score. The graph depicts the normal distribution with mean 0 and standard deviation 1.

Calc: [2nd] [VARS] [InvNorm] area: .2005 = -0.84

A z score (IS/IS NOT) an area under the normal curve.

IS NOT

Finding probabilities associated with distributions that are standard normal distributions is equivalent to...

finding the area of the shaded region representing that probability

Assume that military aircraft use ejection seats designed for men weighing between 135.3 lb and 215 lb. If women's weights are normally distributed with a mean of 172.5 lb and a standard deviation of 45.7 lb, what percentage of women have weights that are within those limits? Are many women excluded with those specifications?

z = x-u/o for min. and max. Calc: [2nd] [VARS] [normalcdf] lower: -999999 lower:-999999 upper: -0.814004 upper: 0.929978 = 0.2090 = 0.8238 Subtract 0.8238 - 0.2090 = .6148 × 100 = 61.48%

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

z = x-u/o Calc: [2nd] [VARS] [normalcdf] lower: -.6 upper: 9999999 = .7257

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

z = x-u/o Calc: [2nd] [VARS] [normalcdf] lower: -1E99 upper: -.6666 = .2525

Assume that adults have IQ scores that are normally distributed with a mean of 98.7 and a standard deviation of 20.6. Find the probability that a randomly-selected adult has an IQ greater than 131.0.

z = x-u/o Calc: [2nd] [VARS] [normalcdf] lower: 1.5679611 upper: 999999 = 0.0584

Assume that adults have IQ scores that are normally distributed with a mean of 100 and the standard deviation of 20. find the probability that a randomly-selected adult has an IQ less than 132.

z = x-u/o Calc: [2nd] [VARS] [normalcdf] lower: -999999 upper: 1.6 = .9452

Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation of 15. Find the probability that a randomly-selected adult has an IQ between 87 and 123.

z = x-u/o ...both sides AREA of shaded region: 0.8849 - 0.1151 = 0.7698

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

z = x-u/o ...of both sides Calc: [2nd] [VARS] [normalcdf] lower: .5333 upper: 2.00 = 0.2742

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

z = x-u/o ...of both sides Calc: [2nd] [VARS] [normalcdf]...of both sides lower: -999999 lower: -99999 upper: -2.00 upper: 1.33 = 0.228 = .9082 AREA of shaded region: 0.9082-0.0228= 0.8854

If you are asked to find the 85th percentile, you are being asked to find _____.

- a data value associated with an area of 0.85 to its left

Assume that adults have IQ scores that are normally distributed with a mean of 99.9 and a standard deviation of 21.9. Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top 75%.

-Convert 25% to a decimal (probability). Calc: [2nd] [VARS] [invNorm] area: 0.25 z = -0.67 x = u + (z × o) x = 85.1

Description of a normal distribution of a random variable...

-Graph centered around the mean -Graph is bell-shaped -Graph is symmetric

Find the indicated z score. The graph depicts the normal distribution with mean 0 and standard deviation 1.

Calc: [2nd] [VARS] [InvNorm] area: 1 - 0.9147 = -1.37

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

Calc: [2nd] [VARS] [invNorm] area: 0.6 z = .2533471011 x = u + (z × o) x = 103.8

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

Calc: [2nd] [VARS] [invNorm] area: 1 - 0.3446 z = .3999409696 x = u + (z × o) x = 106

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. Men have hip breadths that are normally distributed with a mean of 14.8in. and a standard deviation deviation of .9in. Find P99. That is, find the hip breadth for men that separates the smallest 99% from the largest 1%.

Calc: [2nd] [VARS] [invNorm] area: 0.99 z = 2.326347877 x = u + (z × o) x = 16.9

Find the indicated area under the curve of the standard normal distribution then convert it to a percentage. About ____% of the area is between z=-1 and z=1.

Calc: [2nd] [VARS] [normalcdf] lower: -1 upper: 1 =0.6827×100= 68.27%

Find the probability of a bone density test score greater than -1.86...

Calc: [2nd] [VARS] [normalcdf] lower: -1.86 upper: 99999999 =0.9686

Find the probability that a given score is less than 1.52...

Calc: [2nd] [VARS] [normalcdf] lower: 1.52 upper: 99999999 =.064255 1-.064255= 0.9357

Find the probability that a given score is less than -1.69...

Calc: [2nd] [VARS] [normalcdf] lower: -1.69 upper: 9999999 =.9545 1-.9545=0.0455

What conditions would produce a negative z-score?

a z-score corresponding to an area located entirely in the left side of the curve

A survey found that women's heights are normally distributed with mean 63.1 in and and standard deviation 3.3 in. The survey also found that men's heights are normally distributed with mean 67.3 in and a standard deviation 3.8 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 55 inch and a maximum of 63 in. a) Find the percentage of men meeting the height requirement. What does the results suggest about the genders of people who are employed as characters at the amusement park? b) If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements?

a) z = x -u/o ...min. and max. z max. - z min. = 0.1286 × 100 = 12.86 % b) Calc: [2nd] [VARS] [invNorm] area: 0.05 z = -1.64485 x = u + (z × o) x min. = 61.1 x max. = 67.3

Assume that females have pulse rates that are normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute. a) If 1 adult female is randomly selected, find the probability that her pulse rate is LESS THAN 80 beats per minute. b) If 16 adult females are randomly selected find the probability that they have pulse rates with a mean LESS THAN 80 beats per minute.

a) z = x-u/ o = 0.56 Calc: [2nd] [VARS] [normalcdf] lower: -1E99 upper: 0.56 = 7.123

The overhead reach distances of adult females are normally distributed with mean of a 202.5 cm and a standard deviation of 8.cm. a) Find the probability that an individual distance is GREATER THAN 215.90 cm. b) Find the probability that the mean for 15 randomly selected distances is GREATER THAN 201.00 cm.

a) z = x-u/ o = 1.51 Calc: [2nd] [VARS] [normalcdf] lower: -1E99 upper: 1.51 = 0.9344 1 - 0.9344 = 0.0656

A normal distribution is informally described as a probability distribution that is ________ when graphed.

bell-shaped