Answer to Question #301985 in Statistics and Probability for toodles

Question

The probability that a tutor will see 0, 1, 2, 3, or 4 students

x 0 1 2 3 4

P(x) 4/27 1/27 5/9 ? 5/27

(a)      What is the probability that the tutor sees 3 students?                                              

(b)      What is the probability that the number of students the tutor will see is between 1 and 3 inclusive?        

(c)       What is the expected number of students that the tutor will see?

(d)     What is the standard deviation?

 

Answer 1

a) we define p(x=3)

we take 1- ( (4/27) + (1/27) + (5/9) + (5/27) ) = 1- (25/27) = 2/27 = p(x=3)

b) we define p(1≤x≤3 ) = p(x=1) + p(x=2) + p(x=3)

=(1/27) + (5/9) + 2/27) =2/3

c) mean = ( (0 * 4/27) + (1 * 1/27) + (2 * 5/9) + (3 * 2/27) + (4 * 5/27) )

= ( 0 +1/27 + 10/9 + 2/9 + 20/27 )

= 19/9

d) we first obtain the variance as below

= ( ( 0² * 4/27)+ (1² * 1/27) + (2² * 5/9) + (3² * 2/27) + (4² * 5/27) ) - ( (19/9)² )

=( 0 + 1/27 + 20/9 + 12/3 + 80/27 ) - (361/81)

= (83/9) - (361/81)

= 4.765432099

standard deviation = (variance)^1/2 = (4.765432099)^1/2

= 2.182986967