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attashe74 [19]
3 years ago
5

A survey of 1282 student loan borrowers found that 440 had loans totaling more than $20,000 for their undergraduate education. G

ive a 98% confidence interval for the proportion of all student loan borrowers who have loans of $20,000 or more for their undergraduate education. (Give answers accurate to 3 decimal places.)
Mathematics
1 answer:
Xelga [282]3 years ago
6 0

Answer:

The 98% confidence interval of the proportion = (0.312, 0.374)

Step-by-step explanation:

(Give answers accurate to 3 decimal places.)

The formula for Confidence Interval of Proportion is given as:

p ± z × √p(1 - p)/n

Where p = Proportion = x/n

x = 440

n = 1282

p = 440/1282 = 0.34321372854

Approximately = 0.343

z = z-score of 98 % confidence interval

= 2.326

Confidence Interval =

= 0.343 ± 2.326 × √0.343(1 - 0.343)/1282

= 0.343 ± 2.326 × √0.225351/1282

= 0.343 ± 2.326 × √0.00017578081

= 0.343 ± 2.326 × 0.01325823555

= 0.343 ± 0.03083865589

0.343 - 0.03083865589

= 0.31216134411

Approximately = 0.312

0.343 + 0.03083865589

= 0.37383865589

Approximately to = 0.374

Therefore, the 98% confidence interval of the proportion = (0.312, 0.374)

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Answer:  " 15 % " .

_______________________________

     →   " 12 is <u>  15% </u> of 80 " .

_______________________________

Step-by-step explanation:

_______________________________

12 = (n/100) * 80 ;

12 = (80n) /100 ;  Solve for "n:

Note:  80/100 = (80/10) / (100/10) = (8/10) = 0.8  ;

12 = (0.8)n  ;

↔ (0.8n) = 12

Multiply each side of the equation by "10" ; to get rid of the "decimal" ;

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to get:

_______________________________

8n = 120 ;

Divide each side of the equation by "8" ;

to isolate "n" on ONE SIDE of the equation; & to solve for "n" ;

8n/8 = 120/ 8 ;

_______________________________

to get:

_______________________________

n = 15 .

_______________________________

Answer:  " 15 % " .

_______________________________

     →   " 12 is <u>  15% </u> of 80 " .

_______________________________

Hope this helps!

Best wishes!

_______________________________

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