Question

scores for a qualification exam are nromally distibuted, with a mean of 80 and a standard deviation of 10. to be qualfiied for an interview, you must score in the top 10%. what is the lowest score you can earn and still be qualified for an interview

Answer 1

Lowest score earned to be qualified for an interview is 92.82

X : Marks scored in interview

X ~ N(80,100)

Here we need to find x such that P(X > x) = 0.10

using standard normal table,

we get P( z > 1.282) = 0.10

It's always easy to use Standard normal distribution to solve questions of normal distribution because standard normal is special case of normal distribution with mean 0 and standard deviation 1.

To convert x (which follows Normal distribution) to standard normal use: $\frac{x-\mu}{\sigma} \sim N(0,1)$

so, $z = 1.282 = \frac{x-\mu}{\sigma}$

hence,

$x = 1.282 * \sigma + \mu \\x = 1.282 * 10+_80 \\x = 92.82$

Hence Lowest score earned to be qualified for an interview is 92.82

To learn more about Normal Distribution visit:

brainly.com/question/4079902

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