Answer:
97
Step-by-step explanation:
We are asked to find the size of sample to be 95% confident that the error in psychologist estimate of mean reaction time will not exceed 0.01 seconds.
We will use following formula to solve our given problem.
, where,
,
,
.
Substitute given values:
Therefore, the sample size must be 97 in order to be 95% confident that the error in his estimate of mean reaction time will not exceed 0.01 seconds.
Answer:
(a) Shown below.
(b) The probability that the first ball drawn is blue is 0.40.
(c) The probability that only white balls are drawn is 0.36.
Step-by-step explanation:
The balls in the urn are as follows:
Blue balls: B₁ and B₂
White balls: W₁, W₂ and W₃
It is provided that two balls are drawn from the urn, with replacement, and their color is recorded.
(a)
The possible outcomes of selecting two balls are as follows:
B₁B₁ B₂B₁ W₁B₁ W₂B₁ W₃B₁
B₁B₂ B₂B₂ W₁B₂ W₂B₂ W₃B₂
B₁W₁ B₂W₁ W₁W₁ W₂W₁ W₃W₁
B₁W₂ B₂W₂ W₁W₂ W₂W₂ W₃W₂
B₁W₃ B₂W₃ W₁W₃ W₂W₃ W₃W₃
There are a total of N = 25 possible outcomes.
(b)
The sample space for selecting a blue ball first is:
S = {B₁B₁, B₁B₂, B₁W₁, B₁W₂, B₁W₃, B₂B₁, B₂B₂, B₂W₁, B₂W₂, B₂W₃}
n (S) = 10
Compute the probability that the first ball drawn is blue as follows:
Thus, the probability that the first ball drawn is blue is 0.40.
(c)
The sample space for selecting only white balls is:
X = {W₁W₁, W₂W₁, W₃W₁, W₁W₂, W₂W₂, W₃W₂, W₁W₃, W₂W₃, W₃W₃}
n (X) = 9
Compute the probability that only white balls are drawn as follows:
Thus, the probability that only white balls are drawn is 0.36.
Where does that StartFraction ... mess come from? -- I've seen it in other questions.
Comparing that to the general quadratic formula
we see b=-10 (agreeing in both places) a=7 (two places), c=-2
Answer: 7x² - 10x - 2 = 0