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2 years ago

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If 25 servings of guacamole have been sold from a batch, in ounces, what is the standard deviation of how much is left? (Suppose

the servings of guacamole are independent.)

1 answer:

arlik [135]2 years ago

6 0

Answer:

The standard deviation of the the left guacamole is 12.51.

Step-by-step explanation:

As the complete question is not given, thus the complete question is found online and is attached herewith.

From the data

Population mean= $\mu_p$ =2.2 ounces

Population Standard Deviation= $\sigma_p$ =0.4 ounces

Batch mean= $\mu_b$ =80 ounces

Batch Standard Deviation= $\sigma_b$ =7 ounces

As per serving is 2.2 ounces

So for 25 servings, Guacamole used is

25*2.2=55 ounces

Thus the Guacamole left is given as

Batch-55=80-55-25 ounces

As it is given that the servings are independent, thus

Var(Z)=Var(X)+Var(Y)

Here Var(Z) is the variance of the Batch, X is the served guacamole and Y is the left guacamole

Also as variance is given as $V=\mu\sigma^2$ so putting the values

$Var(Z)=Var(X)+Var(Y)\\\mu_b\sigma_b^2=\mu_s\sigma_s^2+\mu_l\sigma_l^2\\80.7^2=55(0.4)^2+25*\sigma_l^2\\\sigma_l^2=3911.2/25\\\sigma_l^2=156.448\\\sigma_l=12.51\\$

So the standard deviation of the the left guacamole is 12.51.

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12. If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95% confident that th

atroni [7]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

Step-by-step explanation:

We have the following info given:

$Confidence= 0.95$ the confidence level desired

$ME =0.03$ represent the margin of error desired

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

The confidence level is 95% or 0.95, the significance is $\alpha=0.05$ and the critical value for this case using the normal standard distribution would be $z_{\alpha/2}=1.96$

Since we don't have prior information we can use $\hat p= 0.5$ as an unbiased estimator

Also we know that $ME =\pm 0.03$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

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2 years ago

1. Three friends pooled their money to purchase a new game system that costs $298. One person

iragen [17]

Answer:

First person: $107

Second person: $98

Third person: $93

Step-by-step explanation:

Let be "f" the amount of money (in dollars) that the first person contributed to the purchase, "s" the amount of money (in dollars) that the second person contributed to the purchase and "t" the amount of money (in dollars) that the third person contributed to the purchase.

With the information given in the exercise, you can set up the following equations:

Equation 1 → $f+s+t=298$

Equation 2 → $s=f-9$

Equation 3 → $t=f-14$

Substitute the Equations 2 and 3 into the Equation 1 and then solve for "f":

$f+(f-9)+(f-14)=298\\\\3f-23=298\\\\f=\frac{321}{3}\\\\f=107$

Finally, substitute the value of "f" into the Equation 2 and then into the Equation 3, in order to find the values of "s" and "t".

Therefore, you get:

$s=107-9\\\\s=98\\\\\\t=107-14\\\\t=93$

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2 years ago

Consider a single spin of the spinner.

alex41 [277]

Answer:

"landing on a shaded portion and landing on a 3"

"landing on an unshaded portion and landing on a number less than 2 "

Step-by-step explanation:

Mutually exclusive means the events will have no intersection.

Let's look at your first choice:

"landing on a shaded portion and landing on an even number"

Landing on a shaded portion would be 1 or 4.

Landing on an even number would be 2 or 4.

There is an intersection (they contain a common element), the 4.

These events are not mutually exclusive.

Let's look at your second choice:

"landing on a shaded portion and landing on a number greater than 3"

Landing on a shaded portion would be 1 or 4.

Landing on a number greater than 3 would be just 4.

There is an intersection; they both contain 4.

These events are not mutually exclusive.

Let's look at your third choice:

"landing on a shaded portion and landing on a 3"

Landing on a shaded portion would be 1 or 4.

Landing on 3 would just be 3.

There is no common elements in the lists listed. These events have no intersection.

These events are mutually exclusive.

Let's look at your fourth choice:

"landing on an unshaded portion and landing on an odd number"

Landing on a unshaded portion would be 2 or 3.

Landing on an odd number would be 1 or 3.

There is an intersection; they both have 3 in common.

These events are not mutually exclusive.

Let's look at your fifth choice:

"landing on an unshaded portion and landing on a number less than 2 "

Landing on an unshaded portion would 2 or 3.

Landing on a number less than 2 would be 1.

There is no intersection.

These events are mutually exclusive.

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2 years ago

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injured runners train on a special track at a rehabilitation center. The track is a square with a half circle on its left and ri

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Answer:

The length of the track is approximately 51.7 ft

The track has <u>three</u> sides of the square and the distance round <u>a half of a</u> complete circle

Step-by-step explanation:

The given track shape and measurements are;

The shape on the left side of the track = Square

The shape on the right side of the track = Half circle

The area of the square on the the left side of the track = 128 square feet

Therefore, from the area, A, of a square of side length, s, which is s × s, and letting the side length of the square = s, we have;

Area of the square portion of the track = s × s = s² = 128 ft²

Therefore, s = √(128 ft²) = 8·√(2) ft.

Whereby the side length of the square is bounded by the diameter of the half circle, we have;

Length of the diameter of the half circle = s = 8·√(2) ft.

The length of the perimeter of the half circle = π·D/2 = π × 8·√(2)/2 = π × 4·√(2) ≈ 17.77 ft.

The perimeter of the track, which is the length of the track is made up of the three sides of the square opposite to the half circle and the circumference of the half circle.

Therefore;

The length of the track = 3 × 8·√(2) ft + π × 4·√(2) ft. = 4·√2×(π+6) ≈ 51.7 ft

The length of the track ≈ 51.7 ft

Which gives;

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5 0

2 years ago