Please help me this is my second to last question
1 answer:
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Answer:
The top 20% of the students will score at least 2.1 points above the mean.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The mean of a certain test is 14 and the standard deviation is 2.5.
This means that
The top 20% of the students will score how many points above the mean
Their score is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84.
Their score is:
16.1 - 14 = 2.1
The top 20% of the students will score at least 2.1 points above the mean.
Answer:
a. The probability is 0.735
b. The probability is 0.6296
c. The probability is 0
Step-by-step explanation:
If we assume a binomial process, the probability that x customer are willing to switch companies is:
nCx is calculated as:
Where n are the 20 cable customers and p is the probability 0.2 that the cable customer are willing to switch companies.
Then, P(x) is:
The probability that between 2 and 5 (inclusive) customers are willing to switch companies is:
P(2≤x≤5) = P(2) + P(3) + P(4) + P(5)
Where P(2), P(3), P(4) and P(5) are equal to:
So, P(2≤x≤5) is:
P(2≤x≤5) = 0.1369 + 0.2054 + 0.2182 + 0.1745 = 0.735
At the same way, the probability that less than 5 customers are willing to switch is:
P(x<5)=P(0)+P(1)+P(2)+P(3)+P(4)
P(x<5)=0.6296
Finally, the probability that more than 16 customers are willing to switch is:
P(x>16)=P(17)+P(18)+P(19)+P(20)
P(x>16)=0