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aleksandrvk [35]
3 years ago
5

Eric is studying people's typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a per

iod when typing. 440 people responded that they leave one space. Create a 90% confidence interval for the proportion of people who leave one space after a period. Round your results to four decimal places.
Mathematics
1 answer:
Otrada [13]3 years ago
3 0

Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given:  Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: \hat{p}=\dfrac{440}{525}\approx0.838

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)

Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)

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Answer:10

Step-by-step explanation:

28-4-4=20

20÷2=10

10+10+4+4=28

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Kristy dad makes 3 times as much per hour as she does. If he makes $48 per hour, how much per hour, how much per hour does krist
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Kristy makes 16 per hour.

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The building below is shown to scale; for every 1 inch of drawing, it is 5 feet in actual distance. The exterior surface area of
VashaNatasha [74]

Answer:

50,000 square inches

Step-by-step explanation:

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8 0
3 years ago
The time taken to assemble a laptop computer in a certain plant is a random variable having a normal distribution of 20 hours an
ludmilkaskok [199]

Answer:

a) 40.13% probability that a laptop computer can be assembled at this plant in a period of time of less than 19.5 hours.

b) 34.13% probability that a laptop computer can be assembled at this plant in a period of time between 20 hours and 22 hours.

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question:

\mu = 20, \sigma = 2

a)Less than 19.5 hours?

This is the pvalue of Z when X = 19.5. So

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

Z = \frac{19.5 - 20}{2}

Z = -0.25

Z = -0.25 has a pvalue of 0.4013.

40.13% probability that a laptop computer can be assembled at this plant in a period of time of less than 19.5 hours.

b)Between 20 hours and 22 hours?

This is the pvalue of Z when X = 22 subtracted by the pvalue of Z when X = 20. So

X = 22

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

Z = \frac{22 - 20}{2}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 20

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

Z = \frac{20 - 20}{2}

Z = 0

Z = 0 has a pvalue of 0.5

0.8413 - 0.5 = 0.3413

34.13% probability that a laptop computer can be assembled at this plant in a period of time between 20 hours and 22 hours.

4 0
3 years ago
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