1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kirill [66]
2 years ago
5

Fewer young people are driving. In , of people under years old who were eligible had a driver's license. Bloomberg reported that

percentage had dropped to in . Suppose these results are based on a random sample of people under years old who were eligible to have a driver's license in and again in . a. At confidence, what is the margin of error and the interval estimate of the number of eligible people under years old who had a driver's license in ?
Mathematics
1 answer:
insens350 [35]2 years ago
6 0

Complete Question

Fewer young people are driving. In 1995, 63.9% of people under years 20 old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample 1,200 of people under 20 years old who were eligible to have a driver's license in 1995 and again in 2016.

a. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 1995?

Margin of error(to four decimal places)

Interval estimate (to four decimal places)

b. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 2016?

Margin of error(to four decimal places)

Interval estimate    to   (to four decimal places)

Answer:

a

  0.6120 <  p <  0.639 + 0.6670

b

  0.3900 <  p < 0.4440

Step-by-step explanation:

Considering question a

   The sample proportion is 1995 is  \^ p_1 = 0.639

    The sample size is  n = 1200

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally the margin of error is mathematically represented as  

     E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }

=>   E =  1.96  * \sqrt{\frac{0.639 (1- 0.639)}{1200} }

=>   E =  0.027

Generally 95% Interval estimate is mathematically represented as  

      \^ p -E <  p <  \^ p +E

=>    0.639 -0.027 <  p <  0.639 + 0.027

=>    0.6120 <  p <  0.639 + 0.6670

Considering question b

   The sample proportion is 1995 is  \^ p_2 = 0.417

    The sample size is  n = 1200

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally the margin of error is mathematically represented as  

     E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }

=>   E =  1.96  * \sqrt{\frac{0.417 (1- 0.417)}{1200} }

=>   E =  0.027

Generally 95% Interval estimate is mathematically represented as  

      \^ p -E <  p <  \^ p +E

=>    0.417 -0.027 <  p <  0.417 + 0.027

=>    0.3900 <  p <   0.4440

You might be interested in
Can someone help and explain ? thank you !
AfilCa [17]
\sf Hello!

\sf y = 2x^{2} + 4x - 3

\sf Discriminant :

= \sf b^{2} - 4ac

= \sf (4)^{2} - 4.(2).(-3)

= \sf 16 - (-24)

= \sf 16 + 24 = \sf 40

\sf Since,
\sf D \:is\:Greater\: than\: 0.

\sf Roots\: are\: Real\: and\: Distinct

\sf Hence,

\sf y = 2x^{2} + 4x - 3\: have\: A.\: Two\: real\: roots

~ \sf iCarl
7 0
2 years ago
How many times is 3^27 less than 9^15?
Sliva [168]

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~~

Question like this are fairly simple...

The one thing you should know, is when ever you deal with questions like this, always go to your calculator first...


But... I will help you with this one...

We know:

9^15 = 205891132094649

3^27 = 7625597484987

So, what is (9^15) / (3^27)???

Well we pull out our calculator, and enter it in, and we get: 27


So...

The answer is: 3^27 is 27x smaller than 9^15

5 0
2 years ago
The mean checkout time in the express lane of a large grocery store is 2.7 minutes, and the standard deviation is 0.6 minutes. T
makkiz [27]

Answer:

a) There is a 69.155 probability that a randomly-selected customer will take less than 3 minutes.

b) There is a 76.11% probability that the average time of two randomly-selected customers will take less than 3 minutes.

c) There is a 90.82% probability that the average time of 64 randomly-selected customers will take less than 2.8 minute.

d) There is a 93.19% probability that the average time of 81 randomly-selected customers will take less than 2.8 minutes.

e) There is a 99.38% probability that the average time of 225 randomly-selected customers will take less than 2.8 minutes.

f) There is a 99.95% probability that the average time of 400 randomly-selected customers will take less than 2.8 minutes.

Step-by-step explanation:

Problems of normally distributed samples can be 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.

In this problem, we have that:

The mean checkout time in the express lane of a large grocery store is 2.7 minutes, and the standard deviation is 0.6 minutes. This means that \mu = 2.7, \sigma = 0.6.

(a) What is the probability that a randomly-selected customer will take less than 3 minutes?

This is the pvalue of Z when X = 3. So:

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

Z = \frac{3 - 2.7}{0.6}

Z = 0.5

Z = 0.5 has a pvalue of 0.6915.

There is a 69.155 probability that a randomly-selected customer will take less than 3 minutes.

(b) What is the probability that the average time of two randomly-selected customers will take less than 3 minutes?

We are now working with the average of a sample, so we must use s instead of \sigma in the formula of Z.

s = \frac{\sigma}{\sqrt{2}} = \frac{0.6}{\sqrt{2}} = 0.4243

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

Z = \frac{3 - 2.7}{0.4243}

Z = 0.71

Z = 0.71 has a pvalue f 0.7611.

There is a 76.11% probability that the average time of two randomly-selected customers will take less than 3 minutes.

(c) The probability that the average time of 64 randomly-selected customers will take less than 2.8 minutes is

This is the pvalue of Z when X = 2.8

s = \frac{\sigma}{\sqrt{64}} = \frac{0.6}{8} = 0.075

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

Z = \frac{2.8 - 2.7}{0.075}

Z = 1.33

Z = 1.33 has a pvalue of 0.9082.

There is a 90.82% probability that the average time of 64 randomly-selected customers will take less than 2.8 minute.

(d) The probability that the average time of 81 randomly-selected customers will take less than 2.8 minutes is.

s = \frac{\sigma}{\sqrt{81}} = \frac{0.6}{9} = 0.067

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

Z = \frac{2.8 - 2.7}{0.067}

Z = 1.49

Z = 1.49 has a pvalue of 0.9319.

There is a 93.19% probability that the average time of 81 randomly-selected customers will take less than 2.8 minutes.

(e) The probability that the average time of 225 randomly-selected customers will take less than 2.8 minutes is.

s = \frac{\sigma}{\sqrt{225}} = \frac{0.6}{15}= 0.04

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

Z = \frac{2.8 - 2.7}{0.04}

Z = 2.50

Z = 2.50 has a pvalue of 0.9938.

There is a 99.38% probability that the average time of 225 randomly-selected customers will take less than 2.8 minutes.

(f) The probability that the average time of 400 randomly-selected customers will take less than 2.8 minutes is.

s = \frac{\sigma}{\sqrt{400}} = \frac{0.6}{20}= 0.03

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

Z = \frac{2.8 - 2.7}{0.03}

Z = 3.30

Z = 3.30 has a pvalue of 0.9995.

There is a 99.95% probability that the average time of 400 randomly-selected customers will take less than 2.8 minutes.

8 0
2 years ago
Four friends are selling snack bars. If snack bars cost $3 each, Munch bars cost $5 each, and Chewies cost $4.50 each, then how
Alinara [238K]
(4×3)+(4×5)+(4×4.5)=12+20+18=50
50÷4=12.50
3 0
2 years ago
Milton needs to find the product of two numbers. one of the numbers is 9. The answer also needs to be 9. how will he solve this
galben [10]
The answer to this problem is one because nine times one equals nine which the answer is still nine
6 0
2 years ago
Other questions:
  • Sara bought 6 packs of baseball cards at one store and 5 packs at another store. There are 17 cards in a pack. How many cards di
    11·2 answers
  • Diego said that the answer to the question "how many groups of 5/6?" are in one is 6/5 or 1 1/5. Do you agree with the same expl
    8·1 answer
  • Help on this please <br> ASAP
    8·2 answers
  • Help! Due very soon!!
    12·1 answer
  • Factorise : 48 + 22x -x²​
    11·2 answers
  • Find the value of x in the figure
    5·1 answer
  • Katherine is 17 years younger than Joe. If Joe is 44 years old, how old is Katherine?
    13·2 answers
  • Enter the decimal equivalent of 11/8
    15·2 answers
  • The number of male students at the local college increased by 250 more male students than the year before. Given
    14·2 answers
  • 9. (a) Seven chairs are stacked in a corner. How many chair legs are left?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!