Answer :
The P(X = 0) = 0.0769 is the probability that none has a food allergy in the News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort.
Here we have;
- (a) P(X <= three) = 0.9658 , P(X<three) = 0.8728
- (b) P(X >= 4) = 0.0342
- (c) P(1 <= X <= three) = 0.6884
- (d) E(X) = 1.25, sigma(X) = 1.089
- (e) P(X=0) = 0.0769
- Step-by-step explanation:
- We are for the reason that X ~ Bin(25, .05) this means that that this may be approximated as a binomial distribution. The formulation for calculating possibility the use of the binomial distribution is:
- P(X=x) = "Cx px qn-x
- wherein n = overall no. of trials
- x = no. of a hit trials
- p = possibility of success
- q = possibility of failure = 1 - p
- We have n = 25 , p = 0.05 and q = 0.95
- (a) P(X<=three)= P(X = 0) + P(X = 1) + P(X = 2) +=^ 25 C_ * (0.05) ^ 0 * (0.95) ^ (25 + 0) +^ 25 C 1 (0.05)¹ (0.95)25-1 +25C2 (0.05)² (0.95)25-2 + ^ 25 C_{three} * (0.05) ^ three * (0.95) ^ (25 - three)
- = 0.2774 + 0.3649 + 0.2305 .
- 0.09302
- P(X <= three) = 0.9658
- P(X < three xss=eliminated xss=eliminated xss=eliminated>
- =^ 25 C_ * (0.05) ^ 0 * (0.95) ^ (25 + 0) +^ 25 C 1 (0.05)¹ (0.95)25-1 +25C2 (0.05)² (0.95)25-2
- = 0.2774 + 0.3649 + 0.2305
- P(X < three>
- (b P(X >= 4) =1-P(X
- =1-( P(X = 0) + P(X = 1) + P(X = 2) +
- P( X = three ))
- = 1 - 0.9658
- P(X >= 4) = 0.0342
- (c) P(1 <= X <= three) = P(X = 1) + P(X = 2) + P(X = three)(0.05)^ 2 (0.95)^ 25-2 +^ 25 C_{three} * (0.05) ^ three * (0.95) ^ (25 - 4)
- = 0.3649 + 0.2305 +
- 0.09302
- P(1 <= X <= three) = 0.6884
- (d) E(X) = np
- = (25)(0.05)
- E(X) = 1.25
- sigma(X) = sqrt(npq)
- = sqrt(25) * (0.05)(0.95)
- sigma(X) = 1.089
- (e) * n = 50 and p = 0.05 We want P(X = 0) : so,
- P(X=0)=^ 50 C_ * (0.05) ^ 0 * (0.95) ^ (50 + 0)
- = (1) ^ * (1)^ * (0.0769)
- P(X = 0) = 0.0769
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