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3 years ago

If a quadratic function is concave down, which of the following is true?

Mathematics

1 answer:

Goshia [24]3 years ago

3 0

Answer:

a is negative i think

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Step-by-step explanation:

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3 years ago

Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 109 and standard deviation 2. (a) What is

allochka39001 [22]

Answer:

a) P(x = 110) = 0

$P( x < 110) = 0.6915 = 69.15\%$

$P( x \leq 110) = 0.6915 = 69.15\%$

b) $P(109 > x > 111) = 1- 0.3413 = 0.6587 = 65.87\%$

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 109

Standard Deviation, σ = 2

We are given that the distribution of blood chloride concentration is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( chloride concentration equals 110)

P(x = 110) = 0

Because in a continuous distribution probability at one point is always zero.

P(chloride concentration is less than 110)

$P(x < 110) = P(z > \displaystyle\frac{110-109}{2}) = P(z < 0.5)$

Calculating the value from the standard normal table we have,

$P( x < 110) = 0.6915 = 69.15\%$

P(chloride concentration is at-most 110)

$P(x \leq 110) = P(z \leq \displaystyle\frac{110-109}{2}) = P(z < 0.5)$

Calculating the value from the standard normal table we have,

$P( x \leq 110) = 0.6915 = 69.15\%$

b) P(chloride concentration differs from the mean by more than 1 standard deviation)

P( 109 > x > 111) = 1 - P( 109 < x < 111)

$P(109 \leq x \leq 111) = P(\displaystyle\frac{109 - 109}{2} \leq z \leq \displaystyle\frac{111-109}{2}) = P(0 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < 0)\\= 0.3413 = 34.13\%$

$P(109 > x > 111) = 1- 0.3413 = 0.6587 = 65.87\%$

Clearly, this probability depend on the values of μ and σ.

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3 years ago