In her monthly tests, Mary got 20 more marks in Mathematics than in English. The total of her
2 answers:
Answer:
English test score: 55
Mathematics test score: 75
Step-by-step explanation:
Let be Mary's score on the English test.
We can say that is her score on the Mathematics test, as the score for the Mathematics test is just the English test score but 20 higher.
Since both scores add up to 130, we can set up an equation to solve for the English test score. Since we said is Mary's score on the Mathematics test,
is the total of her 2 test scores.
This means that Mary got a 55 on her English test score.
To solve for the Mathematics test score we can substitute 55 for in
.
This means Mary got a 75 on her Mathematics test.
Those are the answers
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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
