Answer:
1. 0.048
2. 0.952
3. 0.6465
Step-by-step explanation:
Requirement 1
the probability of no defective calculator is 0.048
Given,
Total calculator = 200
Number of defective = 3
Probability of defective,
p = 3/200
= 0.015
And the probability of non-defective,
q = 1 - p
=1-0.015
=0.985
The Probability distribution of defective follows the normal distribution.
P [X=0] = 〖200〗_(c_0 ) 〖(.015)〗^0 〖(.985)〗^(200-0)
P [X=0] = 0.048
Requirement 2
the probability of no defective is 0.048.
here, the probability of at least one defective means minimum 1 calculator can be defective. So the probability of at least one will be the probability of less than or equal 1.
P [X =less than or equal 1] = 1- P [X=0]
= 1 - 0.048
= 0.952
So the probability of at least one defective is 0.952.
Requirement 3
c) the probability of all defective calculators is 0.6465.
P [X=3] = P[X=0]+ P[X=1]+ P[X=2]+ P[X=3]
Here,
P [X=0] = 0.048
P [X=1] = 〖200〗_(c_1 ) 〖(.015)〗^1 〖(.985)〗^(200-1)
= 0.148228
P [X=2] = 〖200〗_(c_2 ) 〖(.015)〗^2 〖(.985)〗^(200-2)
= 0.2245997
P [X=3] = 〖200〗_(c_3 ) 〖(.015)〗^3 〖(.985)〗^(200-3)
= 0.2257398
So, P [X=3] = 0.048+0.148228+0.2245997+0.2257398
= 0.6465675
So, the probability of all defective calculators is 0.6465.
