Answer:
Option c
Step-by-step explanation:
--The large-sample confidence interval
formula for proportions is valid if np ≥ 15 and n(1-p) ≥ 15. The large sample confidence
interval only contain the true value a certain percentage of the time. A 95% CI will contain the
value 95% of the time. You add 2 successes and 2 failures.
Answer:
a) 0.00019923%
b) 47.28%
Step-by-step explanation:
a) To find the probability of all sockets in the sample being defective, we can do the following:
The first socket will be in a group where 5 of the 38 sockets are defective, so the probability is 5/38
The second socket will be in a group where 4 of the 37 sockets are defective, as the first one picked is already defective, so the probability is 4/37
Expanding this, we have that the probability of having all 5 sockets defective is: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%
b) Following the same logic of (a), the first socket have a chance of 33/38 of not being defective, as we will pick it from a group where 33 of the 38 sockets are not defective. The second socket will have a chance of 32/37, and so on.
The probability will be (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%
Given:
Eighteen 2.5 gallon buckets are needed to fill a cistern with water.
To find:
The constant of variation.
Solution:
If y is directly proportional to x, then
Where, k is constant of variation.
In the given problem, water in cistern (w) is directly proportional to number of buckets (n).
(Capacity of each bucket is 2.5 gallons)
Therefore, the constant of variation is 2.5.
