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3 years ago

Points

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

3 0

Answer:

The amount invested at 9% is $30,000

Step-by-step explanation:

Mardi received an inheritance of $40,000.

Let x be the amount invested at 9%.

So, Amount invested at 10% = 40000-x

Her total annual income from the investments was $3700.

So, $0.09x+0.1(40000-x)=3700$

$0.09x+4000-0.1x=3700$

x=30000

Hence the amount invested at 9% is $30,000

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4 years ago

In the United States, 35% of households own a 4K television. Suppose we take a random sample of 150 households. (a) Describe the

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(a) The distribution of the sample proportion is Normal distribution.

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Step-by-step explanation:

We are given that in the United States, 35% of households own a 4K television.

Suppose we take a random sample of 150 households.

Let $\hat p$ = sample proportion of households who own a 4K television.

The z-score probability distribution for sample proportion is given by;

Z = $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

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(a) The distribution of the sample proportion is related to the Normal distribution.

(b) Probability that in this sample of 150 households more than 50% own a 4K television is given by = P( $\hat p$ > 0.50)

P( $\hat p$ > 0.50) = P( $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ > $\frac{ 0.50-0.35}{\sqrt{\frac{0.50(1-0.50)}{150} } }$ ) = P(Z > 3.67) = 1 - P(Z $\leq$ 3.67)

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Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.67 in the z table which has an area of 0.99988.

Therefore, probability that in this sample of 150 households more than 50% own a 4K television is 0.00012.

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