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Answer:
a) The probability that Jodi scores 78% or lower on a 100-question test is 4%.
b) The probability that Jodi scores 78% or lower on a 250-question test is 0.023%.
Step-by-step explanation:
a) To approximate this distribution we have to calculate the mean and the standard distribution.
The mean is the proportion p=0.85.
The standard deviation can be calculates as:
To calculate the probability that Jodi scores 78% or less on a 100-question test, we first calculate the z-value:
The probability for this value of z is
The probability that Jodi scores 78% or lower on a 100-question test is 4%.
b) In this case, the number of questions is 250, so the standard deviation needs to be calculated again:
To calculate the probability that Jodi scores 78% or less on a 250-question test, we first calculate the z-value:
The probability for this value of z is
The probability that Jodi scores 78% or lower on a 250-question test is 0.023%.