4 Find the standard deviation of a 0:24+1:28+2:24+3:12+4:08+5.04=1.28 squareroot

Question

4 Find the standard deviation of a 0:24+1:28+2:24+3:12+4:08+5.04=1.28 squareroot 1.64 Find the probability that Dr.Smith has fewer than 4 students visit. Find the probability that Dr.Smith has at least one student visit given that fewer than 4 student visit. The Dillon Corporation makes a toy called Jabberin' Joe. It is known from past data that 10% of the Speech chips installed In the toy become defective within a one-year period, today. 14 Jabberin' Joes were sold. What is the probability that exactly 3 of the Installed chips will become delecttve with a year from now? What is the probability that at least one will become defective within the nett year?

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where     
k = number of successes in trials        
n = is the number of independent trials        
p = probability of success on each trial

a)
P( X = 3 ) = ( 14 3 ) * ( 0.1^3) * ( 1 - 0.1 )^11
= 0.1142
b)

P( X < 1)   = P(X=0)          
= ( 14   0 ) * 0.1^0 * ( 1- 0.1 ) ^14
= 0.2288
P( X > = 1 ) = 1 - P( X < 1) = 0.7712

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