Question

1. Let x be the number of errors that appear on a randomly selected page of a book. The table lists the probability distribution of x.

x	0         1          2         3           4
P(x)	.73    .16       .06      .04         .01

1. Find the mean of x                                           b) Standard the deviation

x	P(x)	xP(x)	x2	x2P(X)

2. According to a consulting firm 20% of adults say that they most often use their vacation time for international travel. Assume that this result is true for the current population of all American adults.

1. Using the Binomial formula, find the probability that in a random sample of 12 American
2. adults the number who most often use their vacation time for international travel is

1. Exactly 6

2. None

3. At least 6

4. At most 3

2. Approximate the probability that fewer than 80 have hypertension.

Answer 1

X	P(X)	X*P(X)	X² * P(X)
0	0.7300	0.000	0.000
1	0.1600	0.160	0.160
2	0.0600	0.120	0.240
3	0.0400	0.120	0.360
4	0.0100	0.040	0.160

	P(X)	X*P(X)	X² * P(X)
total sum =	1	0.44	0.92

mean = E[X] = Σx*P(X) =            0.4400
          
E [ X² ] = ΣX² * P(X) =            0.9200
          
variance = E[ X² ] - (E[ X ])² =            0.7264
          
std dev = √(variance) =            0.8523

................

Sample size , n =    12
Probability of an event of interest, p =   0.2

P ( X = 6) = C (12,6) * 0.2^6 * ( 1 - 0.2)^6= 0.0155

P ( X = 0) = C (12,0) * 0.2^0 * ( 1 - 0.2)^12=      0.0687

p(atleast 6) =0.0039

p(atmost 3) =0.7946

....................

THANKS

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