# Correct the final answers to 4

Correct the final answers to 4 decimal places wheneverappropriate.

The score in an test is normally distributed with a mean of 590and a standard deviation of 150. A researcher randomly selectedsome candidates who took the test. If the score of a candidate isless than 480, the candidate is classified as failing the test.

1. Find the probability that a randomly selected candidate failsthe test.
2. Find the value of k if there is10% chance that a randomlyselected candidate student has a score more thank.
3. Suppose a random sample of 13 candidates is selected. Find theprobability that the mean score of them is over 550.
4. Suppose a random sample of 7candidatesis selected. Find theprobability that at most 2 of them with score less than 524.
5. Suppose a random sample of 500 candidates is selected. Find theprobability that at least 350 of them with score more than524.

Given that the score in an test is normally distributed with amean of 590 and a standard deviation of 150.

a) The probability,

b) We need

c) The probability,

d) The probability,

Now use binomial distribution,

e) Here

Now use binomial distribution,

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