# Normal distribution statistics question?

### 2 Answers

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- Wayne DeguManLv 73 months ago
a) We require P(x < 600) => P(z < (600 - 510)/107)

i.e. P(z < 90/107) => P(z < 0.84)

From normal tables we get:

0.79955 => 80%

b) We require P(x > 575) => P(z > (575 - 510)/107)

i.e. P(z > 65/107) => P(z > 0.61)

so, 1 - P(z < 0.61) => 1 - 0.72907

or, 0.27093

So, for a random sample of 1000 we have:

0.27093 x 1000 => 271 score greater than 575

:)>

- 3 months ago
Look up z-scores.

(600 - 510) / 107 = z[1]

90/107 = z[1]

z[1] = 0.8411

z = 0.8411 corresponds to 0.7995 of the graph being below that point, or 79.95%

(575 - 510) / 107 = 65/107 = 0.6075 = (approximately) 0.61

0.7291

72.91% of the graph is below that point

1000 * (1 - 0.7291) =>

1000 * 0.2709 =>

270.9 =>

271

You should expect to find 271 students out of 1000 who make a score greater than 575

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