Ask question

Ask question

All categories

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.

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)

You might be interested in

15x²y³z÷3xy² simplify

umka21 [38]

Answer:

$5xyz$

Step-by-step explanation:

$\frac{15x^2y^3z}{3xy^2}$

Step 1: Divide the numbers

$\frac{15}{3}=5\\\\=\frac{5x^2y^3z}{xy^2}$

Step 2: Simplify

$\frac{x^2}{x}\\\\= x\\\\=\frac{5xy^3z}{y^2}$

Step 3: Simplify

$\frac{y^3}{y^2} = y\\\\=5xyz$

Therefore, the simplified answer is $=5xyz$

7 0

1 year ago

Read 2 more answers

Ice cream usually comes in 1.5-quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v

Troyanec [42]

Answer:

(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c) Because the variance of each variable is dependent on the other.

Step-by-step explanation:

The random variable <em>X</em> and <em>Y</em> are defined as follows:

<em>X</em> = amount of ice cream in the box

<em>Y</em> = amount of ice cream scooped out

The information provided is:

E (X) = 48

SD (X) = 1

V (X) = 1

E (Y) = 2

SD (Y) = 0.25

V (Y) = 0.0625

(a)

The total amount of ice-cream served at the party can be expressed as:

<em>X</em> + 3<em>Y</em>.

Compute the expected value of (<em>X</em> + 3<em>Y</em>) as follows:

$E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54$

Compute the variance of (<em>X</em> + 3<em>Y</em>) as follows:

$V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625$

Then the standard deviation of (<em>X</em> + 3<em>Y</em>) is:

$SD(X + 3Y) =\sqrt{V(X + 3Y)}\\\sqrt{1.5625}\\=1.25$

Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

<em>X</em> - <em>Y</em>.

Compute the expected value of (<em>X</em> - <em>Y</em>) as follows:

$E(X-Y)=E(X)-E(Y)\\=48-2\\=46$

Compute the variance of (<em>X</em> - <em>Y</em>) as follows:

$V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625$

Then the standard deviation of (<em>X</em> - <em>Y</em>) is:

$SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031$

Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

7 0

2 years ago

21.05 divided by 0.2

Valentin [98]

Answer:

Step-by-step explanation:

8 0

1 year ago

Read 2 more answers

If trapezoid JKLM with vertices) (3, 4), K (6,4), L (8, 1) and M (1,1) is rotated 270 degrees counterclockwise, what are the

Stels [109]

Answer:

$J' = (4,-3)$

Step-by-step explanation:

Given

$J = (3, 4)$

$K =(6,4)$

$L = (8, 1)$

$M = (1,1)$

$Rotation = 270CCW$

Required

Determine the new coordinate of J

From rules of rotation,

When a point (x,y) is rotated 270 degrees CCW;

The new point becomes (y,-x)

Considering point J

$J = (3, 4)$

This means

$(x,y) = (3,4)$

Where $x = 3$ and $y = 4$

Using the above rotation rule of

$(x,y) -> (y,-x)$

The coordinates of J' becomes

$J' = (4,-3)$

7 0

2 years ago

Adam is going to make concrete

hodyreva [135]

Answer:

90 kg of stone

Step-by-step explanation:

Adam has 8 x 25 = 200

19 x 22.5 = 427.5

20 x 50 = 1000

He has enough cement and sand

He needs 1090 - 1000 = 90 kg of stone

He needs 2 bags of stone

5 0

2 years ago