Respuesta :
Answer:
The probability that a single student randomly chosen from all those taking the test scores 541 or higher is 0.4052.
Step-by-step explanation:
Let us consider a random variable, [tex]X \sim N (\mu, \sigma^{2})[/tex], then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, [tex]Z \sim N (0, 1)[/tex].
The random variable X is defined as the scores of students on the SAT college entrance examinations at a certain high school.
The mean of the scores was, μ = 534.6 and standard deviation of the scores was, σ = 28.2.
The random variable X follows a Normal distribution.
Compute the probability that a single student randomly chosen from all those taking the test scores 541 or higher as follows:
Apply continuity correction:
P (X ≥ 541) = P (X > 541 + 0.50)
= P (X > 541.50)
[tex]=P(\frac{X-\mu}{\sigma}>\frac{541.5-534.6}{28.2})[/tex]
[tex]=P(Z>0.24)\\=1-P(Z<0.24)\\=1-0.59483\\=0.40517\\\approx0.4052[/tex]
*Use a z-table.
Thus, the probability that a single student randomly chosen from all those taking the test scores 541 or higher is 0.4052.
