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vova2212 [387]
3 years ago
12

The mean student loan debt for college graduates in Illinois is $30000 with a standard deviation of $9000. Suppose a random samp

le of 100 college grads in Illinois is collected. What is the probability that the mean student loan debt for these people is between $31000 and $33000?
Mathematics
1 answer:
Nataly [62]3 years ago
8 0

Answer:

the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

Step-by-step explanation:

Given that:

Mean = 30000

Standard deviation = 9000

sample size = 100

The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:

P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)

P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}}    )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}}    )

P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}}    )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}}    )

P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})

P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})

From Z tables:

P(31000 < X

P(31000 < X

Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

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