A coin is tossed 484 times. Use the normal curve approximation to find the proba

Question

A coin is tossed 484 times. Use the normal curve approximation to find the probability of obtaining (a) between 228 and 255 heads inclusive (b) exactly 246 heads; (c) fewer than 216 or more than 267 heads. Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.) (c) The probability is Round to four decimal places as needed.)

Explanation / Answer

Ans:

Normal approximation:

mean=484*0.5=242

standard deviation=sqrt(484*0.5*(1-0.5)=11

Use continuity correction factor of 0.5

a)

z(227.5)=(227.5-242)/11=-1.318

z(255)=(255.5-242)/11=1.227

P(-1.318<z<1.227)=P(z<1.227)-P(z<-1.318)

=0.8901-0.0937=0.7964

b)

P(x=246)=0.0339

c)

z(215.5)=(215.5-242)/11=-2.409

z(267.5)=(267.5-242)/11=2.318

P(z<-2.409 or z>2.318)=P(z<-2.409)+P(z>2.318)

=0.0080+0.0102=0.0182

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