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Reptile [31]
2 years ago
11

Suppose that a random sample of size 100 is to be selected from a population with mean 50 and standard deviation 8. What is the

probability that a sample mean will be greater than 50.8? Round your answer to three decimal places.
Mathematics
1 answer:
maksim [4K]2 years ago
7 0

Answer:

0.159

Step-by-step explanation:

Given that:

Sample size (n) = 100

Population mean(pm) = 50

Standard deviation (s) = 8

Probability that Sample mean (m) will be greater Than 50.8

Using the relation :

(sample mean - population mean) / (standard deviation /sqrt(n))

P(m > 50.8)

Z = (50.8 - 50) / (8/ sqrt(100))

Z = 0.8 / (8/ 10)

Z = 0.8 / 0.8

Z = 1

P(Z > 1) = 0.15866 ( Z probability calculator)

Hence,

P(Z > 1) = 0.159 ( 3 decimal places)

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Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.
sattari [20]

Answer:

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

x+3y\le 36.

2. Tyler can carry up to 20 pounds of food in his backpack, then

x+1.5y\le 20.

You get the following system of inequalities:

\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.

Now substitute the coordinates of each point:

<u>(1,12):</u>

\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.

False, because first inequality doesn't hold.

<u>(2,10):</u>

\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.

True, both inequalities hold.

<u>(4,5):</u>

\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.

True, both inequalities hold.

<u>(6,10):</u>

\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.

False, because secondt inequality doesn't hold.

<u>(12,8):</u>

\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.

False, because second inequality doesn't hold.

<u>(18,6):</u>

\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.

False, because second inequality doesn't hold.

7 0
3 years ago
SAT verbal scores are normally distributed with a mean of 433 and a standard deviation of 90. Use the Empirical Rule to determin
laila [671]

34% of the scores lie between 433 and 523.

Solution:

Given data:

Mean (μ) = 433

Standard deviation (σ) = 90

<u>Empirical rule to determine the percent:</u>

(1) About 68% of all the values lie within 1 standard deviation of the mean.

(2) About 95% of all the values lie within 2 standard deviations of the mean.

(3) About 99.7% of all the values lie within 3 standard deviations of the mean.

$Z(X)=\frac{x-\mu}{\sigma}

$Z(433)=\frac{433-\ 433}{90}=0

$Z(523)=\frac{523-\ 433}{90}=1

Z lies between o and 1.

P(433 < x < 523) = P(0 < Z < 1)

μ = 433 and μ + σ = 433 + 90 = 523

Using empirical rule, about 68% of all the values lie within 1 standard deviation of the mean.

i. e. ((\mu-\sigma) \ \text{to} \ (\mu+\sigma))=68\%

Here μ to μ + σ = \frac{68\%}{2} =34\%

Hence 34% of the scores lie between 433 and 523.

8 0
3 years ago
What is the axis of symmetry of the function f(x) = –(x + 9)(x – 21)?
ludmilkaskok [199]
First, we have to realize that this is factored form, so we have to put this in standard quadratic form using FOIL, which is a rule mandating how we multiply the numbers here. F stands for First, which means the first number inside the parentheses for both of them, then O means the first number in the first quantity(fancy word for parentheses) multiplied by the last number of the second quantity, and so forth. When you are done, you combine like terms

anyway, you end up with x²-12x-189, but you have to inverse all numbers because of the parentheses in front, so it becomes -x²+12x+189.

Now you can find the axis of symmetry uisng the equation -b=2a (oh yeah, I forgot to mention: the standard quadratic form is a(x)²+b(x)+c already). So you do -12 / -2, which then becomes 6.

The axis of symmetry is 6
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3 years ago
You don't have to draw a line you can just type the volumes in terms of PI and just normal.
Nikolay [14]
Dill pickle 10.6^ units
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3 years ago
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An educator believes that new reading activities for elementary school children will improve reading
Damm [24]

The correct answer to this open question is the following.

Unfortunately, you forgot to attach the scores shown in the back-to-back stem-and-leaf display. So we do not know what the numbers are and we do not have any reference at all

What we can do to help you is to comment on the following general terms.

There have been previous and similar experiments or projects like this in other schools in America. These results suggest that the new activities are better because extra or special reading comprehension programs better prepare students to understand what they are reading and comprehend more than basic ideas of the text.

Students that participate in these programs develop a better sense to understand and like what they are reading, considerably increasing their focus and attention.

These programs have resulted positively when trying to improve the marks of the students, compared to other traditional approaches.

6 0
3 years ago
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