Please help!! What is the solution to the system graphed below?

A normally distributed population has mean 57,800 and standard deviation 750. Find the probability that a single randomly select

Stels [109]

Answer:

(a) Probability that a single randomly selected element X of the population is between 57,000 and 58,000 = 0.46411

(b) Probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = 0.99621

Step-by-step explanation:

We are given that a normally distributed population has mean 57,800 and standard deviation 75, i.e.; $\mu$ = 57,800 and $\sigma$ = 750.

Let X = randomly selected element of the population

The z probability is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) So, P(57,000 <= X <= 58,000) = P(X <= 58,000) - P(X < 57,000)

P(X <= 58,000) = P( $\frac{X-\mu}{\sigma}$ <= $\frac{58000-57800}{750}$ ) = P(Z <= 0.27) = 0.60642

P(X < 57000) = P( $\frac{X-\mu}{\sigma}$ < $\frac{57000-57800}{750}$ ) = P(Z < -1.07) = 1 - P(Z <= 1.07)

= 1 - 0.85769 = 0.14231

Therefore, P(31 < X < 40) = 0.60642 - 0.14231 = 0.46411 .

(b) Now, we are given sample of size, n = 100

So, Mean of X, X bar = 57,800 same as before

But standard deviation of X, s = $\frac{\sigma}{\sqrt{n} }$ = $\frac{750}{\sqrt{100} }$ = 75

The z probability is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

Now, probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = P(57,000 < X bar < 58,000)

P(57,000 <= X bar <= 58,000) = P(X bar <= 58,000) - P(X bar < 57,000)

P(X bar <= 58,000) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ <= $\frac{58000-57800}{\frac{750}{\sqrt{100} } }$ ) = P(Z <= 2.67) = 0.99621

P(X < 57000) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{57000-57800}{\frac{750}{\sqrt{100} } }$ ) = P(Z < -10.67) = P(Z > 10.67)

This probability is that much small that it is very close to 0

Therefore, P(57,000 < X bar < 58,000) = 0.99621 - 0 = 0.99621 .

7 0

3 years ago

A landscaper has enough cement to make a patio with an area of 150 Sq ft. The homeowner wants the length of the patio to be 6 ft

Natasha_Volkova [10]

$A=lw=150\\l=w+6\\(w+6)w=150\\w^2+6w=150\\w^2+6w-150=0\\w=\frac{-b+-\sqrt{b^2-4ac}}{2a}\\w=\frac{-(6)+-\sqrt{(6)^2-4(1)(-150)}}{2(1)}\\w=\frac{-6+-\sqrt{36+600}}{2}\\w=\frac{-6+-\sqrt{636}}{2}\\w=\frac{-6+-2\sqrt{159}}{2}\\w=-3+-\sqrt{159}>0\\w=-3+\sqrt{159}\\\\l=(-3+\sqrt{159})+6\\l=3+\sqrt{159}$

Width = -3 + sqrt(159)
Length = 3 + sqrt(159)

4 0

3 years ago

Jason has 4 gallons of hand sanitizer that contains 25% alcohol. He wants to make a hand sanitizer that contains 50% alcohol. Ho

alexandr402 [8]

Answer:

2 gallons of pure alcohol

Step-by-step explanation:

Let x represent the number of gallons of pure alcohol needed, and create an equation:

4(0.25) + x(1) = (x + 4)0.5

1 + x = 0.5x + 2

x = 0.5x + 1

0.5x = 1

x = 2

So, 2 gallons of pure alcohol should be added.

8 0

3 years ago

The world's biggest rubber band ball has a surface area of 27648. Using 3 as pi for both surface area and volume, estimate the v

jeyben [28]

We know that
surface area of sphere=4*pi*r²
r=√[surface area/(4*pi)]
for surface area=27648
r=√[27648/(4*3)]-------> r=√2304-----> r=48 units

volume of a sphere=(4/3)*pi*r³-----> (4/3)*3*48³---> 442638 units³

the answer is
<span>442368</span>

5 0

3 years ago

Select yes or no to indicate whether a zero must be written in the dividend to find the quotient

neonofarm [45]

Answer:

2.25 divided by 0.6 : Yes and 5.2 divided by 8, 3.63 divided by 3, 71.1 divided by 9 : No

Step-by-step explanation:

We have that when two numbers are divided, they can be written in the form $\frac{p}{q}$ , where p is the dividend and q is the divisor.

Now, when we divide 5.2 by 8, we can write $\frac{5.2}{8}$

Also, the division 3.63 by 3, can be written as $\frac{3.63}{3}$ = 1.21

Further, when we divide 71.1 by 3, we can write $\frac{71.1}{3}$ = 23.7

We can see that above divisions are easy divisions and do not require to write any type of 0 in the numerator.

Moreover, when we divide 2.25 by 0.6, we can write $\frac{2.25}{0.6}$ = $\frac{2.25\times 10}{6}$ .

So, we get that in the last division, we need to write a zero in order to multiply the numerator with 10 for easy division.

Hence, 2.25 divided by 0.6 : Yes and 5.2 divided by 8, 3.63 divided by 3, 71.1 divided by 9 : No

3 0

3 years ago