2 years ago

A fair coin is tossed 5 times in a row. The exact probability of the coin landing heads exactly 2 times is?

Mathematics

2 answers:

makkiz [27]2 years ago

8 0

We can do this using the binomial probability distribution:

5C2 * (1/2)^2 * (1/2)^3 = 10 * 1/32

= 5/16

SpyIntel [72]2 years ago

8 0

The coin has to sides, so there are 2 possible choices given each of the 5 times. 2(5)=10. then, you divide 2 by that number (2/10), which is equal to 1/5

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Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they canno

tensa zangetsu [6.8K]

<h2>Answer with explanation:</h2>

As per given , we have

$\hat{p}=0.48$ , n=331

Critical value for 90% Confidence interval : $z_{\alpha/2}=1.645$

a) Confidence interval :

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.48\pm (1.645)\sqrt{\dfrac{0.48(1-0.48)}{331}}\\\\\approx 0.48\pm0.02746\\\\=(0.48-0.02746,\ 0.48+0.02746)\\\\=(0.45254,\ 0.50746)$

Hence, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot a ord it : $(0.45254,\ 0.50746)$

b) Margin of error : E=1.5%=0.015

Formula for sample size : $n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

For p =0.48 , we have

$n=0.48(1-0.48)(\dfrac{1.645}{0.015})^2=3001.88373333\approx3002$

Hence, the required sample size to survey = 3002

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