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stat week four

QUESTION 1

The standard normal distribution is a normal probability distribution that has a mean of  and

a standard deviation of , and the total area under its density curve is equal to . 

QUESTION 2

Assume that the readings on scietific thermometers are normally distributed with a mean of 0 0C and a standard deviation of 1 0C . A thermometer is randomly selected and tested. Find the probability of the reading less than -.25 in degrees Celsius. (up to four decimal place, please)

  

QUESTION 3

Assume that the readings on scietific thermometers are normally distributed with a mean of 0 0C and a standard deviation of 1 0C . A thermometer is randomly selected and tested. Find the probability of the reading greater than .25 in degrees Celsius. (up to four decimal place, please)

QUESTION 4

Assume that the readings on scietific thermometers are normally distributed with a mean of 0 0C and a standard deviation of 1 0C . A thermometer is randomly selected and tested. Find the probability of the reading greater than -1.05 in degrees Celsius. (up to four decimal place, please)

Assume that the readings on scietific thermometers are normally distributed with a mean of 0 0C and a standard deviation of 1 0C . A thermometer is randomly selected and tested. Find the probability of the reading less than 1.93 in degrees Celsius. (up to four decimal place, please)

QUESTION 6

Assume that the readings on scietific thermometers are normally distributed with a mean of 0 0C and a standard deviation of 1 0C . A thermometer is randomly selected and tested. Find the probability of the reading between -2.67 and 1.28 in degrees Celsius. (up to four decimal place, please)

QUESTION 7

Assume that the readings on scietific thermometers are normally distributed with a mean of 0 0C and a standard deviation of 1 0C . A thermometer is randomly selected and tested. Find the probability of the reading between 2.70 and 3.13 in degrees Celsius. (up to four decimal place, please)

QUESTION 8

For a standard normal distribution, find the percentage of data that are more than 2 standard deviations away from the mean. (up to two decimal place, please)

QUESTION 9

Assume that the readings on the thermometers are normally distributed with a mean of 0  C and a standard deviation of 1  C. A thermometer is randomly selected and tested. If 1.7% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others. (up to two decimal place, please)

QUESTION 10

Assume that human body temperatures are normally distributed with a mean of 98.20 0F and a standard deviation of 0.62 0F. Physicians want to select a minimum temperature for requiring further medical tests. what should that temperature be, if we want only 5% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.)  (up to one decimal place, please)

QUESTION 11

Assume that the heights of women are normally distributed with a mean given by 63.6 inches and a standard deviation given by 2.5 inches. The Beanstalk club, a social organization for tall people, has a requirement that women must be at least 70 inches tall. What percentage of women meet that requirement? (up to four decimal place, please)

QUESTION 12

Assume that the heights of women are normally distributed with a mean given by 63.6 inches and a standard deviation given by 2.5 inches. The U.S. Army requires women's heights to be between 58 inches and 80 inches. What percentage of women meet that requirement? (up to four decimal place, please)

QUESTION 13

The intelligence quotient (IQ) is based on a test of aptitude and is often used as a measure of an individual’s intelligence. The distribution of IQ scores is approximately normally distributed with mean 100 and standard deviation 15. What is the z-value of 80? (up to three decimal place, please)

QUESTION 14

The distribution of IQ scores is approximately normally distributed with mean 100 and standard deviation 15. What is the probability to have an IQ score 140 or above?

a.

0.9962

b.

0.9924

c.

0.0076

d.

0.0038

QUESTION 15

The distribution of IQ scores is approximately normally distributed with mean 100 and standard deviation 15. What is the probability to have an IQ score between 110 and 120?

a.

.7486

b.

.9082

c.

.0918

d.

.1596

QUESTION 16

Five numbers are given: 85, 79, 82, 73, 78. Assume that samples of size 2 are randomly selected with replacement from the above population of five numbers. Find the mean of the sampling distribution. 

a.

b.

c.

d.

QUESTION 17

Five numbers are given: 85, 79, 82, 73, 78. Assume that samples of size 2 are randomly selected with replacement from the above population of five numbers. Calculate the standard deviation of the sampling distribution of sample mean. (up to  four  decimal place, please)

QUESTION 18

Assume that men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb. If one man is randomly selected, find the probability that his weight is less than 167 lb.(up to  four  decimal place, please)

QUESTION 19

Assume that men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb. If 36 man is randomly selected, find the probability that they have a mean weight less than 167 lb.(up to  four  decimal place, please)

QUESTION 20

Assume that men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb. If 4 man is randomly selected, find the probability that they have a mean weight between 160 lb and 180 lb.(up to  four  decimal place, please)

STAT WEEK FOUR

QUESTION 1

The

standard

normal

distribution

is

a

normal

probability

distribution

that

has

a

mean

of

and

a

standard

deviation

of

,

and

the

total

area

under

its

density

curve

is

equal

to

.

QUESTION 2

Assume

that

the

readings

on

scietific

thermometers

are

normally

distributed

with

a

mean

of

0

0

C

and

a

standard

deviation

of

1

0

C

.

A

thermometer

is

randomly

selected

and

tested.

Find

the

probability

of

the

reading

less

than

-

.25

in

degrees

Celsius.

(up

to

four

decimal

place,

please)

QUESTION 3

Assume

that

the

readings

on

scietific

thermometers

are

normally

distributed

with

a

mean

of

0

0

C

and

a

standard

deviation

of

1

0

C

.

A

thermometer

is

randomly

selected

and

tested.

Find

the

probability

of

the

reading

greater

than

.25

in

degrees

Celsius.

(up

to

four

decimal

place,

please)

QUESTION 4

Assume

that

the

readings

on

scietific

thermometers

are

normally

distributed

with

a

mean

of

0

0

C

and

a

standard

deviation

of

1

0

C

.

A

thermometer

is

randomly

selected

and

tested.

Find

the

probability

of

the

reading

greater

than

-

1.05

in

degrees

Celsius.

(up

to

four

decimal

place,

please)

Assume

that

the

readings

on

scietific

thermometers

are

normally

distributed

with

a

mean

of

0

0

C

and

a

standard

deviation

of

1

0

C

.

A

thermometer

is

randomly

selected

and

tested.

Find

the

probability

of

the

reading

less

than

1.93

in

degrees

Celsius.

(up

to

four

decimal

place,

please)

QUESTION 6

Assum

e

that

the

readings

on

scietific

thermometers

are

normally

distributed

with

a

mean

of

0

0

C

and

a

standard

deviation

of

1

0

C

.

A

thermometer

is

randomly

selected

and

tested.

Find

the

probability

of

the

reading

between

-

2.67

and

1.28

in

degrees

Celsius.

(up

to

four

decimal

place,

please)

QUESTION 7

Assume

that

the

readings

on

scietific

thermometers

are

normally

distributed

with

a

mean

of

0

0

C

and

a

standard

deviation

of

1

0

C

.

A

thermometer

is

randomly

selected

and

tested.

Find

the

probability

of

the

reading

between

2.70

and

3.13

in

degrees

Celsius.

(up

to

four

decimal

place,

please)

QUESTION 8

For a standard normal distribution, find the percentage of data that are more than 2 standard deviations away from

the mean. (up to two decimal place, please)

STAT WEEK FOUR

QUESTION 1

The standard normal distribution is a normal probability distribution that has a mean of

and

a standard deviation of

, and the total area under its density curve is equal to

.

QUESTION 2

Assume that the readings on scietific thermometers are normally distributed with a mean of 0

0

C and a standard

deviation of 1

0

C . A thermometer is randomly selected and tested. Find the probability of the reading less than -.25

in degrees Celsius. (up to four decimal place, please)

QUESTION 3

Assume that the readings on scietific thermometers are normally distributed with a mean of 0

0

C and a standard

deviation of 1

0

C . A thermometer is randomly selected and tested. Find the probability of the reading greater than

.25 in degrees Celsius. (up to four decimal place, please)

QUESTION 4

Assume that the readings on scietific thermometers are normally distributed with a mean of 0

0

C and a standard

deviation of 1

0

C . A thermometer is randomly selected and tested. Find the probability of the reading greater than -

1.05 in degrees Celsius. (up to four decimal place, please)

Assume that the readings on scietific thermometers are normally distributed with a mean of 0

0

C and a standard

deviation of 1

0

C . A thermometer is randomly selected and tested. Find the probability of the reading less than 1.93

in degrees Celsius. (up to four decimal place, please)

QUESTION 6

Assume that the readings on scietific thermometers are normally distributed with a mean of 0

0

C and a standard

deviation of 1

0

C . A thermometer is randomly selected and tested. Find the probability of the reading between -2.67

and 1.28 in degrees Celsius. (up to four decimal place, please)

QUESTION 7

Assume that the readings on scietific thermometers are normally distributed with a mean of 0

0

C and a standard

deviation of 1

0

C . A thermometer is randomly selected and tested. Find the probability of the reading between 2.70

and 3.13 in degrees Celsius. (up to four decimal place, please)

QUESTION 8

For a standard normal distribution, find the percentage of data that are more than 2 standard deviations away from

the mean. (up to two decimal place, please)