A particular type of mouse's weights are normally distributed, with a mean of 359 grams and a standard deviation of 33 grams. If you pick one mouse at random, find the following: (round all probabilities to four decimal places)
a) What is the probability that the mouse weighs less than 405 grams?
b) What is the probability that the mouse weighs more than 461 grams?
c) What is the probability that the mouse weighs between 406 and 461 grams?
d) Is it unlikely that a randomly chosen mouse would weigh less than 405 grams?
i. No, the likelihood exceeds 50%
ii. No, the likelihood exceeds 5%
iii. Yes, the likelihood is less than 50%
iv. Yes, the likelihood is less than 5%
e) What is the cutoff for the heaviest 10% of this type of mouse?
Answer:
Following are the responses to the given points:
Step-by-step explanation:
Given:
[tex]\mu = 359 \ \ \ \ \ \sigma = 33\\\\[/tex]
Using formula:
[tex]\to P(X = x) = P\left ( z < \frac{x-\mu }{\sigma } \right )[/tex]
For point a:
[tex]\to x= 406\\\\P(X < 406 ) = P\left ( z < \frac{406-359 }{33 } \right )\\\\[/tex]
[tex]= P\left ( z <1.4242\right )\\\\= 0.9222[/tex]
For point b:
[tex]\to x= 461\\\\P(X > 461 ) = P\left ( z > \frac{461 -359 }{33 } \right )\\\\[/tex]
[tex]= 1 - P\left ( z < 3.0909 \right )\\\\= 1 - 0.9990\\\\= 0.0001[/tex]
For point c:
[tex]\to x= 406\ \ and \ \ 461\\\\P(406 <X < 461 ) = P(X < 461) - P (X < 406)\\\\[/tex]
[tex]= 0.9990 - 0.9222\\\\= 0.0768\\\\[/tex]
For point d:
[tex]P(X < 406) = 0.9222 = 92.22 \%\ that \ is \ greater \ than\ 50\%[/tex]
Hence, the correct choice is "i".
For point e:
[tex]\to P(X > z) = 0.1\\\\\to 1 - P(X < z) = 0.1\\\\\to P(\frac{x-\mu }{\sigma }) = 0.9\\\\\to \frac{x-359}{33 } = 1.28\\\\ \to x = 401.24\\\\[/tex]
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Answer: Her highest score is on turn two because she used a negative number over a positive and a positive is more than a negative.
Step-by-step explanation:
10>-16
Which expression shows the difference when subtracting these 2 polynomials?
(5x – 9x +11)-(-2x2+ 3x – 2)
a 7x2-12x+13
b 3x2+8x+9
A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10.2 hours per week. Is the amount of time greater than that for this year
Answer:
mu = the population true mean time spent by teenagers playing computer game this year
Step-by-step explanation:
Dear student, there is no much information given to answer this question but we will try as much as possible to explain (what is the parameter) of the true mean.
In 1990s;
μ = 10.2 hours/week
From the information given,we understand that the parameter is linked to the population, and we're looking for the population average time spent playing computer games by teens in the current situation.
In this situation, the population parameter is the population true mean mu = the population true mean.
Judy scored 30 points in the champion game. She scored three 3-point baskets and five 1-point baskets. How many 2-point baskets did she score?
Answer:
eight two point baskets
Step-by-step explanation:
3 points = 9 points
1 points = 5 points
9+5= 14
30-14= 16
= 16/2
=8
what is the greatest common factor of 20a^2 12a^2 and 8a
Answer:
4a
Step-by-step explanation:
Am I correct? K
Thanks for helping!
PLEASEEE CHECK ME WORK!
Answer:
yes you are correct on all of them good job
Wat is the average number between 1,000, 2300,1000,2600
Answer:
here summation x = sum of all number
f(x)=10x-15 g(x)=2x-3 Find: (f/g)(x)
The function operation (f/g)(x) in the functions f(x) = 10x-15 and g(x) =2x-3 is 5.
What is the function operation (f/g)(x) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
f( x ) = 10x - 15g( x ) = 2x - 3( f / g )( x ) = ?First, we replace the function designators in f/g with the actual functions.
(f / g )(x) = f(x) / g(x)
(f / g )(x) = ( 10x - 15 ) / ( 2x - 3 )
Now, factor out 5 from 10x and -15
(f / g )(x) = 5( 2x - 3 ) / ( 2x - 3 )
Cancel the common factor of 2x - 3
(f / g )(x) = 5( 1 ) / ( 1 )
(f / g )(x) = 5 / 1
(f / g )(x) = 5
Therefore, the function operation (f/g)(x) equals 5.
Learn more about functions here: brainly.com/question/2541698
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SOMEONE PLEASE HELP ME ASAP ILL MARK BRAINLIEST!!!!
Answer:
90 answer plss brainless me
Write a variable expression for this amount.
fourteen times x
Type the correct answer.
Answer:
14x
Step-by-step explanation:
14x = 14 x (x) = 14(x)
Estimate the sum of the decimals below by rounding to the nearest whole number.
6.802
6 1844
+ 6.318
Answer:
19
Step-by-step explanation:
6.802 = 7
6.1844 = 6
6.318 = 6
7 + 6 + 6 = 19
I hope this helps!
The measure of (angle) 6 is 120. The measure of (angle) 5 is 100. What is the measure of (angle) 4
Answer:
80
Step-by-step explanation:
4x20=80
find the value of x.
please help! :)
Answer:
x=9
Step-by-step explanation:
You weigh a random sample of adult golden retrievers and get the following results: 55, 64, 58, 61, 69, 64, 59, 69, 72, and 65. Which answer gives a 98% confidence interval for the mean of the population
Answer:
The 98% confidence interval for the mean of the population is (59, 68.2).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{55+64+58+61+69+64+59+69+72+65}{10} = 63.6[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(55-63.6)^2+(64-63.6)^2+(58-63.6)^2+(61-63.6)^2+(69-63.6)^2+(64-63.6)^2+(59-63.6)^2+(69-63.6)^2+(72-63.6)^2+(65-63.6)^2}{10}} = 5.142[/tex]
Confidence interval:
We have the standard deviation for the sample, and thus, we use the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.821
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.821\frac{5.142}{\sqrt{10}} = 4.6[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 63.6 - 4.6 = 59
The upper end of the interval is the sample mean added to M. So it is 63.6 + 4.6 = 68.2.
The 98% confidence interval for the mean of the population is (59, 68.2).
convert 1 2/5 x 2/3 into a mixed number
The sum of three numbers is 910. One of the numbers, x, is 60% greater than the sum of the other two numbers. What is the value of x?
Answer:
I don't know I'm sorry I tried to found answers but I couldn't
there is a gamecjwkjcs x,x dzvfbhjhv bzdhu vhaj vuy vrjahfv jhadfv ahjza v zjhv
Answer:
it is babylonia huming by chris
(-6, 10), (-6,1),(1, 10) What are the coordinates of the fourth vertex of the rectangle? Enter your answer by filling in the boxes.
Answer:
(1,1)
Step-by-step explanation:
Happy To Help!Please answer what is 1 2 3 4 5 no links I forgot to do my homework
1. 40°
2. 50°
3. 45°
4. a. draw a line from angle P to downward but make it so it can cut angle OPQ from the half
b. 70°
c. angle TPQ = angle OPQ ÷2
angle TPQ = 140÷2= 70°
Solve the following system using any method.
−5x+7y=10
−9x−4y=18
Answer:
-2,0
Step-by-step explanation:
See the steps below:)
5/6 + 4/6
a) 1/6
b) 9/12
c)1 3/6
d) 1 2/6
Answer:
this is the answer Hope's it helps
HELP!!!!
5^m x (5^-7)^m = 5^12
Answer:
not sure lol but, like it up
Step-by-step explanation:
1. How much salt and baking powder together is needed to make 36 cup cakes?
Answer:
too much salt will not bring taste to the cup cakes
Step-by-step explanation:
$150/1 sq ft x 20 sq ft
Answer:
$3000
Step-by-step explanation:
$150 / 1 sq ft * 20 sq ft
$150 / 1 sq ft = this means $150 per square feet :
Given that there area 20 Square feets, then
Cost in $ will be :
$150 * 20 sq feet
= $3000
help me on this. I’d appreciate it
Answer:
36
Step-by-step explanation:
The cost of cleaning up pollution in a stream is given by C = 37000 100−p, where C is the cost in dollars to clean p percent of the stream. Find and interpret C(20)
Answer:
$462.5
Step-by-step explanation:
Given the cost function expressed as;
C = 37000/100−p
To get C(20), we will substitute p = 20 into the expression and get C as shown;
C(20) = 37000/100-20
C(20) = 37000/80
C(20) = 462.5
Hence the cost needed to clean 20% of the stream is $462.5
Enter the coordinates of the solution of these two linear equations.
Answer:
(-4,2) are solution coordinates
This is the point in which these two lines intersect
Can someone help me??
A= 346.5cm^2, thats the answer
what is the perimeter measured in centimeters of the rectangle pictured below do not include units in your answer
Answer:
183
Step-by-step explanation:
The perimeter of the rectangle measured in centimeters is 26 cm.
What is Perimeter?Perimeter of a straight sided figures or objects is the total length of it's boundary.
Given a rectangle in the figure.
The length of the rectangle = 7 cm
Width of the rectangle = 6 cm
We have to find the perimeter of the rectangle.
Perimeter of the rectangle = 2(l + w), where l is the length and w is the width.
Perimeter = 2(7 + 6)
= 2 × 13
= 26 cm
Hence the perimeter is 26 cm.
Learn more about Perimeter here :
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