verifica care dintre urmatoarele numere sunt cuburi perfecte:2 la puterea a 8, 27, 64, 5 la puterea 48, si 7 la puterea 225

62% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 48 owned dogs are r

dedylja [7]

Answer:

a) 0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b) 0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c) 0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d) 0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

Step-by-step explanation:

To solve this question, we use the binomial probability distribution, and also it's approximation to the normal distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

62% of owned dogs in the United States are spayed or neutered.

This means that $p = 0.62$

48 owned dogs are randomly selected

This means that $n = 48$

Mean and standard deviation, for the approximation:

$\mu = E(x) = np = 48*0.62 = 29.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{48*0.62*0.38} = 3.36$

a. Exactly 30 of them are spayed or neutered.

This is P(X = 30), which is not necessary the use of the approximation.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 30) = C_{48,30}.(0.62)^{30}.(0.38)^{18} = 0.1180$

0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b. At most 33 of them are spayed or neutered.

Now we use the approximation. This is, using continuity correction, $P(X \leq 33 + 0.5) = P(X \leq 33.5)$ , which is the pvalue of Z when X = 33.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{33.5 - 29.76}{3.36}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c. At least 31 of them are spayed or neutered.

Using continuity correction, this is $P(X \geq 31 - 0.5) = P(X \geq 30.5)$ , which is 1 subtracted by the pvalue of Z when X = 30.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30.5 - 29.76}{3.36}$

$Z = 0.22$

$Z = 0.22$ has a pvalue of 0.5871

1 - 0.5871 = 0.4129

0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d. Between 24 and 30 (including 24 and 30) of them are spayed or neutered.

This is, using continuity correction, $P(24 - 0.5 \leq X \leq 30 + 0.5) = P(23.5 \leq X \leq 30.5)$ , which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 23.5.

X = 30.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30.5 - 29.76}{3.36}$

$Z = 0.22$

$Z = 0.22$ has a pvalue of 0.5871

X = 23.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{23.5 - 29.76}{3.36}$

$Z = -1.86$

$Z = -1.86$ has a pvalue of 0.0314

0.5871 - 0.0314 = 0.5557

0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

8 0

3 years ago

20 in

alukav5142 [94]

Answer:

C

Step-by-step explanation:

This question can simply be answered by the process of elimination. All of the other answers have numbers behind the first number of the decimal. when you are rounding to the nearest tenth, you will have no numbers behind the decimal except 1. They will look like this:

11.70

23.30

45.60

So, since we are looking for the nearest tenth, we would choose C because it is the only one that is rounded.

8 0

2 years ago

An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the fou

Burka [1]

Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

$\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})$

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, $\frac{2}{3}$

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

= 1.66 ft

Width of the box = (8 - 2x) = 8 - 1.34

= 6.66 ft

Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

6 0

3 years ago

Owens birthday cake weights 6 T. (LOL). How many pounds does it weigh?

Inga [223]

Answer:

12000 pounds is your answer

8 0

3 years ago

A ladder leans against the side of a house. The angle of elevation of the ladder is 70 when the bottom of the ladder is 16ft fro

makkiz [27]

46.78

Step-by-step explanation:

you divide 16 by the cos of 70 and it turns out to be 46.78

3 0

3 years ago