Answer in Statistics and Probability for Randi Carpenter #88387

Dishonest-Coin Principle

Let X denote the number of heads in n tosses of a coin (assume “ngeq30)”. Let p denote the probability of heads on each toss.Then, X has an approximately normal distribution with mean “mu=ncdot p” and standard deviation “sigma =sqrt{ncdot pcdot (1-p)}”.

We have that “p=0.1, n=400”. Then “mu=400cdot 0.1=40, sigma =sqrt{400cdot 0.1cdot (1-0.1)}=6.”

a) at most 40 with defective speakers

“z={x-mu over sigma}={40.5-40 over 6}=0.083333”

“P(Xleq40)=P(X<40.5)=P(Z<0.083333)=0.533207”

b) Most than 52 with defective speakers

“z={x-mu over sigma}={52.5-40 over 6}=2.083333”

“P(X>52)=P(X>52.5)=0.018610”