A batch of 200 calculators contains 3 defective units. What the probability that a sample of three calculators will have/be
a) no defective calculators
b) at least one defective calculator
c) all defective calculators

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.

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.