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Natalija [7]
3 years ago
8

A survey found that​ women's heights are normally distributed with mean 63.2 in. and standard deviation 2.4 in. The survey also

found that​ men's heights are normally distributed with a mean 67.2 in. and standard deviation 2.7. Complete parts a through c below. a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in. and a maximum of 6 ft 2 in. Find the percentage of women meeting the height requirement?
Mathematics
1 answer:
Effectus [21]3 years ago
8 0

Answer: 99.51%

Step-by-step explanation:

Given : A survey found that​ women's heights are normally distributed.

Population mean : \mu =63.2  \text{ inches}

Standard deviation: \sigma= 2.4\text{ inches}

Minimum height = 4ft. 9 in.=4\times12+9\text{ in.}=57\text{ in.}

Maximum height = 6ft. 2 in.=6\times12+2\text{ in.}=74\text{ in.}

Let x be the random variable that represent the women's height.

z-score : z=\dfrac{x-\mu}{\sigma}

For x=57, we have

z=\dfrac{57-63.2}{2.4}\approx-2.58

For x=74, we have

z=\dfrac{74-63.2}{2.4}\approx4.5

Now, by using the standard normal distribution table, we have

The probability of women meeting the height requirement :-

P(-2.58

Hence, the percentage of women meeting the height requirement = 99.51%

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Cory, Josh and Dan went shopping for Halloween treats. Cory bought 3 chocolate pumpkins, 4 masks and 8 candy witches. He spent $
bija089 [108]

Answer:

The cost of chocolate pumpkins is $1.89, masks cost $5.75 and candy witches cost $1.62

Step-by-step explanation:

Let x represent the cost of chocolate pumpkins, y the cost of masks and z the cost of candy witches.

Cory shopping can be represented as:

3x + 4y + 8z = 41.63      (1)

Josh shopping can be represented as:

6x + 2y + 14z = 45.52    (2)

Dan shopping can be represented as:

8x + 3y + 25z = 72.87    (3)

The equations in matrix form is:

\left[\begin{array}{ccc}3&4&8\\6&2&14\\8&3&25\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}41.63\\45.52\\72.87\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}3&4&8\\6&2&14\\8&3&25\end{array}\right] ^{-1}\left[\begin{array}{c}41.63\\45.52\\72.87\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1.89\\5.75\\1.62\end{array}\right]

The cost of chocolate pumpkins is $1.89, masks cost $5.75 and candy witches cost $1.62

7 0
2 years ago
what is the ratio for the volumes of two similar spheres given that the ratio of their radii is 4:7 A.)343:64 B.)49:16 C.)16:49
quester [9]

Answer:

Volume of the similar sphere be 64 :343 .

Option (D) is correct.

Step-by-step explanation:

Formula

Volume\ of\ a sphere = \frac{4}{3}\pi r^{3}

As given

The volumes of two similar spheres given that the ratio of their radii is 4:7 .

Let us assume that the x be the scalar multiple of the radi .

Radius of first sphere = 4x

Radius of second sphere = 7x

Putting the values in the formula

Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 4x\times 4x\times 4x

Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 64x^{3}

Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 7x\times 7x\times 7x

Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 343x^{3}

Thus

\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{\frac{4\pi\times 64x^{3}}{3}}{\frac{4\pi\times 343x^{3}}{3}}

\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{64}{343}

Therefore the ratio of the volume of the similar sphere be 64 :343 .

Option (D) is correct .

5 0
2 years ago
Read 2 more answers
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