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marshall27 [118]

3 years ago

14

Sid is 300$ in debt. He needs to get the debt down to no more than 100$ within the next 8 months. If he pays the same amount eac

h month, what is the minimum he must pay off each month to manage this?

1 answer:

jek_recluse [69]3 years ago

7 0

He has to pay a minimum of $25 each month

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The heights of 40 randomly chosen men are measured and found to follow a normal distribution. An average height of 175 cm is obt

AVprozaik [17]

Answer:

95% two-sided confidence interval for the true mean heights of men is [168.8 cm , 181.2 cm].

Step-by-step explanation:

We are given that the heights of 40 randomly chosen men are measured and found to follow a normal distribution.

An average height of 175 cm is obtained. The standard deviation of men's heights is 20 cm.

Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average height = 175 cm

$\sigma$ = population standard deviation = 20 cm

n = sample of men = 40

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

So, 95% confidence interval for the true mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

<u>95% confidence interval for </u> $\mu$ = [ $\bar X-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ]

= [ $175-1.96 \times }{\frac{20}{\sqrt{40} } }$ , $175+1.96 \times }{\frac{20}{\sqrt{40} } }$ ]

= [168.8 cm , 181.2 cm]

Therefore, 95% confidence interval for the true mean height of men is [168.8 cm , 181.2 cm].

<em>The interpretation of the above interval is that we are 95% confident that the true mean height of men will be between 168.8 cm and 181.2 cm.</em>

3 0

3 years ago

20 POINTS! Please help

LUCKY_DIMON [66]

Hey! I believe the answer is A. Have a nice/great day! :-)

4 0

3 years ago

The Community College Survey of Student Engagement reports that 46% of the students surveyed rarely or never use peer or other t

kap26 [50]

Answer:

d) No, this would not be unusual because 46% is only 1.2 standard errors from 40%.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If the z-score is higher than 2 or lower than -2, X is unusual.

In this question:

Mean = 40%. So $\mu = 0.4$

Standard error = 5%. So $\sigma = 0.05$

Is 46% unusual?

We have to find Z when X = 0.46. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.46 - 0.4}{0.05}$

$Z = 1.2$

1.2 is lower than 2, that is, it is only 1.2 standard deviations from the mean. So 46% is not unusual.

So the correct answer is:

d) No, this would not be unusual because 46% is only 1.2 standard errors from 40%.

3 0

3 years ago

2. The price of 1 kg potatoes increased from

mestny [16]

Answer:

+75%

Step-by-step explanation:

20 * x = 35

x = 35 / 20

x = 1.75

3 0

3 years ago

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What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Leviafan [203]

-x^2+2x+3=x^2-2x+3 add x^2 to both sides

2x+3=2x^2-2x+3 subtract 2x from both sides

3=2x^2-4x+3 subtract 3 from both sides

2x^2-4x=0 factor

2x(x-2)=0

So x=0 and 2

3 0

3 years ago

Read 2 more answers