1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Thepotemich [5.8K]
3 years ago
9

In Lake Erie, walleye fish are abundant. The lengths of walleyes follow a Normal distribution with a mean of 31 inches and a sta

ndard deviation of 3.6 inches. Based on this information, which of the following statements is true?a. Approximately 32% of walleyes have lengths less than 27.4 inches.b. Approximately 95% of walleyes have lengths greater than 23.8 inches.c. Approximately 16% of walleyes have lengths longer than 38.2 inches.d. Approximately 84% of walleyes have lengths less than 34.6 inches.d. Approximately 2.5% of walleyes have lengths between 31 inches and 34.6 inches.
Mathematics
1 answer:
AlladinOne [14]3 years ago
5 0

Answer:

d. Approximately 84% of walleyes have lengths less than 34.6 inches.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 31

Standard deviation = 3.6

a. Approximately 32% of walleyes have lengths less than 27.4 inches.

27.4 is one standard deviation below the mean.

By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. Of the other 32% more than 1 standard deviation from the mean, 16% of the lengths are less than 27.4 and 16% are greather than 31+3.6 = 34.6.

So approximately 16% of walleyes have lengths less than 27.4 inches, which means that this statement is false.

b. Approximately 95% of walleyes have lengths greater than 23.8 inches.

23.8 is two standard deviations below the mean.

By the Empirical Rule, 95% of the measures are within 2 standard deviations of the mean. Of the 5% that is more than 2 standard deviations from the mean, 2.5% is greater than 2 standard deviations above the mean(greater than 38.2, in this problem), and 2.5% is lower than 2 standard deviations below the mean(lower than 23.8 in this problem).

So 2.5% of walleyes have lengths lower than 23.8 and 100-2.5 = 97.5% have lengths greater than 23.8, which means that this statement is false.

c. Approximately 16% of walleyes have lengths longer than 38.2 inches.

38.2 is two standard deviations above the mean.

By the Empirical Rule, 95% of the measures are within 2 standard deviations of the mean. Of the 5% that is more than 2 standard deviations from the mean, 2.5% is greater than 2 standard deviations above the mean(greater than 38.2, in this problem), and 2.5% is lower than 2 standard deviations below the mean(lower than 23.8 in this problem).

So 2.5% of walleyes have lengths longer than 38.2 inches, which means that this statement is false.

d. Approximately 84% of walleyes have lengths less than 34.6 inches.

34.6 is one standard deviation above the mean.

The empirical rule is symmetric, which means that 50% of the measures are above the mean and 50% of the meausures are below the mean.

Also, 68% of the measures are within 1 standard deviation of the mean. Of those, 34% are between one standard deviation below the mean and the mean, and 34% are between the mean and one standard deviation above the mean.

So, 50% below the mean, plus 34% between the mean and 34.6 means that approximately 84% of the walleyes have lengths less than 34.6 inches, which means that this statement is true.

e. Approximately 2.5% of walleyes have lengths between 31 inches and 34.6 inches.

31 is the mean

34.6 is one standard deviation above the mean.

By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. Of those, 34% are between one standard deviation below the mean and the mean, and 34% are between the mean and one standard deviation above the mean.

So 34% of walleyes have lengths between 31 inches and 34.6 inches, which means that this statement is false.

You might be interested in
What does the slope formula mean
Virty [35]

Answer:

I honestly used google.

Step-by-step explanation:

It means: In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".

8 0
3 years ago
Read 2 more answers
Using radicals , write an equivalent expression for the expression y 1/5
Nutka1998 [239]
Hope there are y^(1/5) so than this mean 5 index radical of y 

hope helped 
3 0
3 years ago
.
Nitella [24]
Radius is 3 in and height is 9 in. Volume is 3²×9π=81π=254.34 cu in.
4 0
3 years ago
Read 2 more answers
11.Use the exponential regression equation that best fits the data
Marysya12 [62]

Answer:

73.5 ....................

6 0
3 years ago
Read 2 more answers
1)simplify the expression (2x)^4 2)the perimeter of a rectangular is twice the sum of its length and its width. the perimeter is
Marta_Voda [28]
(2x)^4=16x^4
------------------------------------------
2(l+w)=16\\
l=2w+2\\\\
2(2w+2+w)=16\\
6w+4=16\\
6w=12\\
w=2\\\\
l=2\cdot2+2\\
l=6

-------------------------------------------
-3+yi=x+6i\Rightarrow x=-3 \wedge y=6
5 0
3 years ago
Other questions:
  • The distance d (in miles) that you can see to the horizon with your eye level h feet above the water is given by d=3h2−−−√. You
    13·1 answer
  •  how do i solve equation for x  T=1/3 (x-y+z)
    14·2 answers
  • You have a total of 35 coins, all nickels ($0.05) and quarters ($0.25). The total value is $5.75. Find the number of nickels, n,
    13·1 answer
  • Simplify the polynomial: 2[4x-5(2x-1)]
    13·1 answer
  • What is the answer to the following equations
    13·1 answer
  • Which of the following exponential functions goes through the points (1, 20) and (2, 80)?
    7·2 answers
  • I need help please be quick​
    9·1 answer
  • Laura tiene una tarifa de telefono en la que paga solo por el tiempo que dura cada llamada .Si un minuto cuesta o,16€ ysu ultima
    9·1 answer
  • What is the value of 3^ -2 as a fraction
    10·1 answer
  • nine times a number y subtracted from 85 is seven times the sum of four and y . ( i need the equation for this )
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!