A coin is weighted so that there is a 58.8% chance of it landing on heads when f

Question

A coin is weighted so that there is a 58.8% chance of it landing on heads when flipped. The coin is flipped 15 times.

Find the probability that the number of flips resulting in "heads" is at least 5 and at most 10.

Round your answer to 4 decimal places.

The mean salary of people living in a certain city is $37500 with a standard deviation of $2322. A sample of 53 people is selected at random from those living in the city.

Find the probability that the mean income of the sample is within $500 of the population mean.

Round your answer to 4 decimal places.

Explanation / Answer

a)

P(heads =5) =15C5*(0.588)5(0.412)10 = 0.0297

P(heads =6) =15C6*(0.588)6(0.412)9 =0.0708

P(heads =7) =15C7*(0.588)7(0.412)8 = 0.1298

P(heads =8) =15C8*(0.588)8(0.412)7 =0.1853

P(heads =9) =15C9*(0.588)9(0.412)6 =0.2057

P(heads =10) =15C10*(0.588)10(0.412)5 = 0.1761

P("heads" is at least 5 and at most 10 ) = 0.0297+0.0708+0.1298+0.1853+0.2057+0.1761 = 0.7974

b)standard deviation of sample mean = 2322/53 = 318.95

mean = 37500

mean income of the sample is within $500 of the population mean i.e in (mean - 500,mean+500)

z for mean -500 is (-500)/318.95 = -1.5676,pvalue = 0.058487

z for mean +500 is (500)/318.95 = 1.5676,pvalue = 0.941513

P(x<mean-500) = 0.058487

P(x<mean+500) = 0.941513

P(mean-500<x<mean+500) = 0.941513-0.058487 =0.883

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