Question

Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 490 and 560

Answer 1

$P(490 < X < 560)$= 0.3133

Given: μ = 560

σ = 90  

To find: P (490 < X < 560)

Normal distributions are symmetric, unimodal, and asymptotic. A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. It's always easy to solve questions in terms to standard normal

Hence, converting normal distribution to standard normal gives:

P(490 < X < 560)  = $P(\frac{560-560}{90}$≤ $\frac{X-\mu}{\sigma} < \frac{640-560}{90})$

                              = P(0 ≤ Z < 0.888)

                               = P (z<0.89) - P(z  ≤ 0)

Using standard normal table,

= 0.8133 - 0.5

P(490 < X < 560) = 0.3133

To learn more about Normal Distribution, visit:

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