Answer:
The probability is
Step-by-step explanation:
The total number of students are 200.
number of full timers is 110 and number of part timers is 90.
number of male students is 90 and number of female students is 110.
Let the probability of part timers be P(B).
P(B) = =
Let the probability of female part timers be P(A)
P(A) =
now, the final probability is
=
=
Answer:
The conditions necessary for the analysis are met.
The probability the newspaper’s sample will lead them to predict defeat is 0.7881
Step-by-step explanation:
We are given;
population proportion; μ = 52% = 0.52
Sample size;n = 400
The conditions are;
10% conditon: sample size is less than 10% of the population size
Success or failure condition; np = 400 x 0.52 = 208 and n(1 - p) = 400(1 - 0.52) = 192.
Both values are greater than 10
Randomization condition; we assume that the voters were randomly selected.
So the conditions are met.
Now, the standard deviation is gotten from;
σ = √((p(1 - p)/n)
where;
p is the population proportion
n is the sample size
σ is standard deviation
Thus;
σ = √((0.52(1 - 0.52)/400)
σ = √((0.52(0.48)/400)
σ = 0.025
Now to find the z-value, we'll use;
P(p^ > 0.5) = P(z > (x - μ)/σ)
Thus;
P(p^ > 0.5) = P(z > (0.5 - 0.52)/0.025)
This gives;
P(p^ > 0.5) = P(z > - 0.8)
This gives;
P(p^ > 0.5) = 1 - P(z < -0.8)
From the table attached we have a z value of 0.21186
Thus;
P(p^ > 0.5) = 1 - 0.21186 = 0.7881
Thus, the probability the newspaper’s sample will lead them to predict defeat is 0.7871
