Section 7.2 Homework

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Section 7.2 Homework

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Section 7.2 Homework

 

1.  A normal population has mean

μ = 8

and standard deviation

σ = 6

.  Find the proportion of the population that is between 5 and 20.  Round the answers to at least four decimal places.

The proportion of the population that is between 5 and 20 is _____

 

2.   A normal population has mean

μ = 40 

and standard deviation 

σ = 9

(a) What proportion of the population is between 20 and 30?

(b) What is the probability that a randomly chosen value will be between 35 and 45?

Round the answers to at least four decimal places.
 
 
The proportion of the population between 20 and 30 is _______
 
The probability that a randomly chosen value will be between 35 and 45 is ________
 
 
3. Check our blood pressure: In a recent study, the Centers for Disease Control and prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.4 mmHg and a standard deviation of 9.8 mmHg. Round the answers to four decimal places.

Part 1 of 4
Your Answer is correct
 
 

(a) What proportion of women have blood pressures lower than 65 mmHg?

The proportion of women who have blood pressures lower than 65 mmHg is ______.
 
 
 

(b) What proportion of women have blood pressures between 72 mmHg and 90 mmHg?

The proportion of women who have blood pressures between

72 mmHg and 90 mmHg is ______

 

(c) A diastolic blood pressure greater than 90 mmHg is classified as hypertension (high blood pressure). What proportion of women have hypertension?

The proportion of women who have hypertension is ________.
 

(d) Is it unusual for a woman to have a blood pressure lower than 63 mmHg?

It ____ unusual because the probability of a woman having blood pressure lower than _____ is __________ 

4.  Fish story: According to a report by the U.S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the Arolik River in Alaska is 481 millimeters with a standard deviation of 43 millimeters. Assume these lengths are normally distributed.

(a) What proportion of six-year-old rainbow trout are less than 443 millimeters long?

(b) What proportion of six-year-old rainbow trout are between 396 and 520 millimeters long?

(c) Is it unusual for a six-year-old rainbow trout to be less than 397 millimeters long?

Round the answers to at least four decimal places.

 
The proportion of six-year-old rainbow trout less than 443 millimeters long is _______
 
The proportion of six-year-old rainbow trout between 396 and 520 millimeters long is ________
 
It ____ unusual because the probability of a six-year-old rainbow trout less than 397 millimeters long is ______
 
 
5.  A normal population has mean 

μ = 55

and standard deviation 

σ = 14. 

Find the value that has 45% of the population above it. Round the answer to at least one decimal place.

 
The value that has 45% of the population above it is _____
 
 
6. A normal population has mean

μ = 51 

and standard deviation

σ = 12

.  Find the values that separate the middle 75% of the population from the top and bottom 12.5%. 

 
 
The values that separate the middle 75% of the population above from the top and bottom 12.5% are ____ and ____.  Enter the answers in ascending order and round to one decimal place.
 
 
 7.   Fish story: According to a report by the U.S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the Arolik River in Alaska is 482 millimeters with a standard deviation of 42 millimeters. Assume these lengths are normally distributed. Round the answers to at least two decimal places.

(a) Find the 58th percentile of the lengths.

(b) Find the 87th percentile of the lengths.

(c) Find the first quartile of the lengths.

(d) A size limit is to be put on trout that are caught. What should the size limit be so that 15% of six-year-old trout have lengths shorter than the limit?

 
 
Your Answer is correct
 
 

Find the 58th percentile of the lengths.

The 58th percentile of the lengths is ___________

 

Find the 87th percentile of the lengths.

The 87th percentile of the lengths is ______

 

Find the first quartile of the lengths.

The first quartile of the lengths is ______
 
 
 
 
 
 
 
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This question is taken from Math 138 – Statistics » Fall 2021 » Homeworks