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3 years ago

9

A cone has a diameter of 30 in. and a slant height of 17 in.

1 answer:

prisoha [69]3 years ago

3 0

Use the given formula :

$V=\frac{1}3\pi r^2h=\frac{1}3\pi (\frac{D}2)^2h$ where $D$ is the diameter.

By Pythagoras, $h=\sqrt{17^2-(30/2)^2}=8\text{ in}$

Hence $V\approx\frac{3.14}3*15^2*8=\boxed{1884.0\text{ in}^3}$

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A simple random sample of size n=14 is obtained from a population with μ=64 and σ=19.

madam [21]

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a) A. The population must be normally distributed

b) P(X < 68.2) = 0.7967

c) P(X ≥ 65.6) = 0.3745

Step-by-step explanation:

a) The population is normally distributed having a mean ( $\mu_x$ ) = 64 and a standard deviation ( $\sigma_x$ ) = $\frac{19}{\sqrt{14} }$

b) P(X < 68.2)

First me need to calculate the z score (z). This is given by the equation:

$z=\frac{x-\mu_x}{\sigma_x}$ but μ=64 and σ=19 and n=14, $\mu_x=\mu=64$ and $\sigma_x=\frac{ \sigma}{\sqrt{n} }=\frac{19}{\sqrt{14} }$

Therefore: $z=\frac{68.2-64}{\frac{19}{\sqrt{14} } }=0.83$

From z table, P(X < 68.2) = P(z < 0.83) = 0.7967

P(X < 68.2) = 0.7967

c) P(X ≥ 65.6)

First me need to calculate the z score (z). This is given by the equation:

$z=\frac{x-\mu_x}{\sigma_x}$

Therefore: $z=\frac{65.6-64}{\frac{19}{\sqrt{14} } }=0.32$

From z table, P(X ≥ 65.6) = P(z ≥ 0.32) = 1 - P(z < 0.32) = 1 - 0.6255 = 0.3745

P(X ≥ 65.6) = 0.3745

P(X < 68.2) = 0.7967

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3 years ago