Whats the nth term in this sequence <br> 1 , 7, 13, 19

The navy reports that the distribution of waist sizes among male sailors is approximately normal, with a mean of 32.6 inches and

grandymaker [24]

Answer:

a) 87.49%

b) 2.72%

Step-by-step explanation:

Mean of the waist sizes = u = 32.6 inches

Standard Deviation of the waist sizes = $\sigma$ = 1.3 inches

It is given that the Distribution is approximately Normal, so we can use the z-distribution to answer the given questions.

Part A) A male sailor whose waist is 34.1 inches is at what percentile

In order to find the percentile score of 34.1 we need to convert it into equivalent z-scores, and then find what percent of the value lie below that point.

So, here x = 34.1 inches

The formula for z score is:

$z=\frac{x-u}{\sigma}$

Using the values in the above formula, we get:

$z=\frac{34.1-32.6}{1.3}=1.15$

Thus, 34.1 is equivalent to z score of 1.15

So,

P( X ≤ 34.1 ) = P( z ≤ 1.15 )

From the z-table we can find the probability of a z score being less than 1.15 to be: 0.8749

Thus, the 87.49 % of the values in a Normal Distribution are below the z score of 1.15. For our given scenario, we an write: 87.49% of the values lie below 34.1 inches.

Hence, the percentile rank of 34.1 inches is 87.49%

Part B)

The regular measure of waist sizes is from 30 to 36 inches. Any measure outside this range will need a customized order. We need to find that what percent of the male sailors will need a customized pant. This question can also be answered by using the z-distribution.

In a normal distribution, the overall percentage of the event is 100%. So if we find what percentage of values lie between 30 and 36, we can subtract that from 100% to obtain the percentage of values that are outside this range and hence will need customized pants.

First step is again to convert the values to z-scores.

30 converted to z scores will be:

$z=\frac{30-32.6}{1.3}=-2$

36 converted to z score will be:

$z=\frac{36-32.6}{1.3}=2.62$

So,

P ( 30 ≤ X ≤ 36 ) = P ( -2 ≤ z ≤ 2.62 )

From the z table, we can find P ( -2 ≤ z ≤ 2.62 )

P ( -2 ≤ z ≤ 2.62 ) = P(z ≤ 2.62) - P(z ≤ -2)

P ( -2 ≤ z ≤ 2.62 ) = 0.9956 - 0.0228

P ( -2 ≤ z ≤ 2.62 ) = 0.9728

Thus, 97.28% of the values lie between the waist sizes of 30 and 36 inches. The percentage of the values outside this range will be:

100 - 97.28 = 2.72%

Thus, 2.72% of the male sailors will need custom uniform pants.

The given scenario is represented in the image below. The black portion under the curve represents the percentage of male sailors that will require custom uniform pants.

3 0

4 years ago

Rewrite the following radical expressions as equivalent exponential expressions.<br> b. 2(4√3)

IRISSAK [1]

Answer:

$2^{3} .3^{\frac{1}{2} }$ .

Step-by-step explanation:

Here in this problem, we have to rewrite a radical expression as an equivalent exponential expression.

The radical expression is 2(4√3)

Now, 2 ( 4√3)

=( 2 × 4) √3 {Since all the terms are in product form so, we can rearrange it}

= ( 2× 2²) × √3

=2³√3 {Since we know the formula from the property of exponent, xᵃ . xᵇ = x⁽ᵃ⁺ᵇ⁾ }

= $2^{3} .3^{\frac{1}{2} }$ .

Therefore, $2^{3} .3^{\frac{1}{2} }$ is the required equivalent exponential form. (Answer)

8 0

4 years ago

a city council has 12 members. Five are democratss and seven are republicans. How many ways can a four member comitte be selecte

Nostrana [21]

Answer: 495ways

Step-by-step explanation:

Selecting some b people from a group of people are based on combination principle.

If we are selecting "r'' people from a total number of 'n' people, we will have;

nCr = n!/(n-r)!r!

Since 4 people are to be selected from a committee of 5democrats and 6republicans,

Note that the question is not specific as to how many from Republicans and Democrats to select that will make the 4people,

Therefore, the selection can be done in this manner

- 0people from democrats and 4peoples from Republicans

5C0 × 7C4 = 5!/5!0! × 7!/3!4!

= 1×35= 35ways

- 1people from democrats and 3peoples from Republicans

5C1 × 7C3 = 5×35 = 175ways

- 2peoples from democrats and 2peoples from Republicans

5C2 × 7C2 = 10 × 21 = 210ways

- 3peoples from democrats and 1people from Republicans

5C3 × 7C1 = 10 × 7 = 70ways

- 4peoples from democrats and 0people from Republicans

5C4 × 7C0 = 5 × 1 = 5ways

Adding all possible combinations

35+175+210+70+5

= 495ways

3 0

3 years ago

The circle passes through the point (-1.-6). What is its radius?

Mice21 [21]

Answer:

Step-by-step explanation:

Not enough information.

7 0

3 years ago

Kym used the integer tiles to find the sum of (–3) + 6. The line showed that the answer is negative 3. Which of the following do

Yuki888 [10]

Answer:

Kai built the bookshelf shown below. The bookshelf is 48 inches tall with a solid board on the back, and EACH shelf measures 18 inches wide by 24 inches long. If Kai wants to paint all the surfaces, including the undersides of both shelfs and the base, as well as both sides of the bookshelf’s back and sides, how many square FEET will he paint?

Step-by-step explanation:

8 0

3 years ago

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Whats the nth term in this sequence 1 , 7, 13, 19