(1 point)
The number of eggs that a female house fly lays during her lifetime is normally distributed with mean 790 and standard deviation 92.
Random samples of size 98 are drawn from this population, and the mean of each sample is determined. What is the probability that
the mean number of eggs laid would differ from 790 by less than 30? Round your answer to four decimal places.
Answer:
0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean 790 and standard deviation 92.
This means that [tex]\mu = 790, \sigma = 92[/tex]
Samples of 98
This means that [tex]n = 98, s = \frac{92}{\sqrt{98}}[/tex]
What is the probability that the mean number of eggs laid would differ from 790 by less than 30?
This is the pvalue of Z when X = 790 + 30 = 820 subtracted by the pvalue of Z when X = 790 - 30 = 760. So
X = 820
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{820 - 790}{\frac{92}{\sqrt{98}}}[/tex]
[tex]Z = 3.23[/tex]
[tex]Z = 3.23[/tex] has a pvalue of 0.9994
X = 760
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{760 - 790}{\frac{92}{\sqrt{98}}}[/tex]
[tex]Z = -3.23[/tex]
[tex]Z = -3.23[/tex] has a pvalue of 0.0006
0.9994 - 0.0006 = 0.9988
0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.
Let f(x)=x^2-6 and g(x)=7x
Please help thank you
solve for x in 2.3^x-81-3^x
Answer:
===================
Solved by graphing: x =~ 3.711448
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You can use a graphing calculator, or numerical
what is the value of. view image
Directions: Type your answer in the box below without using the ($) symbol.
Wesley had $792.38 in his checking account. He made the following transactions:
• He bought groceries at Food Lion using his debit card for $58.62.
• He received $50.00 for his birthday and deposited the money into his checking account.
• He made a withdrawal at the ATM from his checking account in the amount of $120.00. • He purchased a pair of shoes from the mall using his debit card in the amount of $64.98.
What was the final balance in his checking account after these transactions?
Answer:
Wesley's final balance in his checking account after these transactions is $598.78.
Step-by-step explanation:
792.38 - 58.62 + 50 - 120 - 64.98 = 598.78
I am really confused what a mean is in math
Answer:
A mean in math is when you have a set of numbers, you add up all numbers of the set and then divide that sum by the total amount of numbers.
Example: 3,6,8,9
3+6+8+9=26
26/4 (because there is four numbers)
26/4= 6.5
So the mean of that set will be 6.5
Step-by-step explanation:
What is 4x minus x squared?
Answer:
3x^2
Step-by-step explanation:
the answer isssssssssssssssssssssssssss 3x^2.
y=3x+2 find the oder pairs
Answer:
x y
0 2
1 5
Step-by-step explanation:
14ab5 - 2ab5 + 4b2 +b
Answer:
80ab + 9b
Step-by-step explanation:
Step 1: 14 x 5 + 2ab x 5 + 4b x 2 + b
Then......
Multiple the numbers: 14 x 5 = 70
Step 2: = 70ab + 2 x 5ab + 4 x 2b + b
Then......
Multiple the numbers: 2 x 5 = 10
Step 3: = 70ab + 10ab + 4 x 2b + b
Then......
Multiple the numbers: 4 x 2 = 8
Step 4: = 70 ab + 10ab + 8b + b
Then......
Add similar elements: 70ab + 10ab = 80ab
Step 5: = 80ab + 8b + b
Then......
Add similar elements: 8b + b = 96
80ab + 9b
( I HOPE THIS HELPED!)
In which quadrants is sine positive?
O A. I and IV
B. I and III
C. II and IV
D. I and II
Answer:
D. I and II
Step-by-step explanation:
In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.
The solution is, sine is positive in, D. I and II. Option (D) is correct because, In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles.
here, we have,
We are given to select the correct answer from the options provided.
The rule of signs for the trigonometric ratios in the four quadrants are as follows :
Quadrant I : All the three ratios, tangent, sine and cosine are positive.
Quadrant II : Only sine is positive, cosine and tangent are negative.
Quadrant III : Only tangent is positive, sine and cosine are negative.
Quadrant IV : Only cosine is positive, sine and tangent are negative.
so, we get,
In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.
Therefore, using the above rules, we can say that the options (B), (C) and (A) are incorrect.
so, we have,
Option (D) is correct because, In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.
To learn more about trigonometric relations click :
brainly.com/question/14450671
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The volume of the Moon is about 2.8 x 10^10 cubic kilometers. The volume of Earth is about 1.9 x 10^12 cubic kilometers. The number of Moons that can fit inside Earth can be found by dividing Earth's volume by the Moon's volume. About how many Moons can fit inside Earth?
Answer:
50 moons can fit inside Earth.
Step-by-step explanation:
The Volume of Earth is
1.09 × 10 ^12
cubic kilometres
The Volume of The Moon is
2.18 x 10^ 10
cubic kilometers
Hence the number of Moons that can fit in Earth is
Step-by-step explanation:
what is the arc length of s in the figure below
Answer:
2.18ft
Step-by-step explanation:
what is the arc length of s in the figure below
Length of the arc = theta/360 * 2πr
r is the radius = 1ft
theta = 125 degrees
Substitute into the formula
Length of the arc = 125/360 * 2(3.14)* 1
Length of the arc = 785/360
Length of the arc = 2.18ft
Hence the length of the arc is 2.18ft
Hey guys!!! I forgot how to do this :/ lol
whats 10+4÷2?
Answer:
12
Step-by-step explanation:
Simplify 4x + 3x² + x² - 3x
Answer:
[tex]x + {4x}^{2} [/tex]
Step-by-step explanation:
simplify by combining like terms
4x - 3x = x
[tex]3x ^{2} + {x}^{2} = {4x}^{2} [/tex]
we're left with
[tex]x + {4x}^{2} [/tex]
Answer:
4x²+x
Step-by-step explanation:
4x-3x+3x²+x²
4x minus 3x is x and 3x² +x² is 4x²
therefore,
4x²+x
where is the whole number in 34.50
Answer:
34
Step-by-step explanation:
7x+4=25
two step equation
Answer:
x = 3
Step-by-step explanation:
7x + 4 = 25
7x + 4 - 4 = 25 - 4
7x = 21
x = 3
Answer:
x = 3
Step-by-step explanation:
Hey! Hope this helps you!
Have a nice day <3
Which of the following expressions is equivalent to (13 + 2) (13 - 2)?
a. 152 +112
b. 15² – 11²
c. 132 +22
d. 132 - 22
Answer:
d. 13^2 - 2^2
Step-by-step explanation:
The product of a sum and a difference is a difference of squares.
(13 + 2)(13 - 2) = 13^2 - 2^2
Answer: d. 13^2 - 2^2
How many meters are in a exameter?
Answer:
1E18 OR 10^18
Step-by-step explanation:
The formula is multiply the length by 1e+18
NEEDED ASAP WILL GIVE BRAINLIEST TO BEST ANSWER
Answer:
for 14 is Surface are =2*(7*5+7*3+5*3)= 142 feet cubefor 13 Surface are= 2*(9*7.2+9*9+7.2*9)= 421 m cube
What is the mean of the set of data given below? 13 8 9 6 10 8
Answer:
Mean = The numbers added up and divided by the number of numbers.
Step-by-step explanation:
= (13 + 8 + 9 + 6 + 10 + 8) / 6
= 54 / 6
= 9
The mean is 9.
What formula can be used to find circumference? Choose all that apply. *
Cat
2r
nd
2nd
Answer:
circumference =pi ×diameter
OR
pi × radius × 2
luego le digo 4yo1 xkw k
Answer:
okay luego le digo 4yo1 xkw k
Step-by-step explanation:
Simply each answer .
Answer:
मुझे गर्म गले पसंद है
Step-by-step explanation:
X^2+3x-18 what are the zeros of r(x)?
Answer:
Step-by-step explanation:
18 has factors of 9 and 2 or 6 and 3
Those factors must differ by 3, so 6 and 3 in some order is your answer.
(x + 6) (x - 3) = r(x)
You have to make x a value that turns the factor into 0.
x + 6 = 0
x = - 6
x - 3 = 0
x = 3
So the zeros are (3,0) and (- 6,0)
Combine like terms:
7x + 3x + 4y - X+.5y
Answer:
9x + 4.5y if .5y is a decimal point, 9x + 9y if the dot is a typo
Step-by-step explanation:
If the dot is real,
7x + 3x + 4y - x + 0.5y
10x + 4y - x + 0.5y
10x - x + 4y + 0.5y
9x + 4.5y
If the dot is a typo,
7x + 3y + 4x - x + 5y
10x + 4y - x + 5y
10x - x + 4y + 5y
9x + 9y
Answer:
the answer is 9x + 9y
7x + 3x + 4y - x + 5y
7x + 3x - x + 4y + 5y
10x - x + 4y + 5y
9x + 9y
Assume your home is assessed at $245,000. You have a $171,000 loan for 25 years at 6 percent. Your property tax rate is 1.4 percent of the assessed value. In year one, you would pay $10,260 in mortgage interest and $3,430 in property tax (1.4 percent on $245,000 assessed value).
Answer: $3,833.20
Step-by-step explanation:
Mortgages interest and property tax are both federal deductions so they will reduce taxes:
= 10,260 + 3,430
= $13,690
The tax saving is therefore:
= 13,690 * tax rate
= 13,690 * 28%
= $3,833.20
Trinity can run around the perimeter of her school's sports field in 4.75 minutes. It takes Jing 1.2 minutes longer. Alberto can run around the perimeter of the field in 5.9 minutes. Which correctly compares Jing's running time to Alberto's running time?
14x1/2 consider the expression
Answer: 7
Step-by-step explanation:
14*1=14
14/2=7
Can somebody please help me with this ?
Answer:
8x, 2x^2, 6xy, 5y.
Step-by-step explanation:
Hello, 5x+3x would be 8x since 5+3 is 8. 7x^2-5x^2 would be 2x^2 since 7-5 is 2 (exponents stay the same). 2xy+4xy is 6xy since 2+4 is 6. Lastly, 8y-3y is 5y since 8-3 is 5.
Someone explain and help me do this for me I really need the help
Answer:
74.13
6×10=60
A=pi r^2
3.14×3^2=28.26
28.26/2 =14.13 (because it is half a circle)
14.13+60=74.13
not sure if that is correct but that is what i got