Answer to Question #205772 in Statistics and Probability for angel egaran

Question

1. The recent Statistics test scores of Grade 1 pupils of Baesa Elementary School is normally distributed with a mean of 41 and a standard deviation of 6. If a random sample of 60 pupils is selected and their scores are recorded, (A) find the probability that their average score is greater than 40 but less than 42, and, (B) determine the number of sample means falling below 40. (25points). Note the standard error formula is n

Answer 1

A)We need to compute $\Pr(40 \leq \bar X \leq 42)$ . The corresponding z-values needed to be computed are:

$Z lower= \frac{X{_{1}-\mu }}{\sigma /\sqrt{n}}$ =$\frac{40-41 }{6 /\sqrt{60}}=-1.29$

Z upper= $\frac{42-41 }{6 /\sqrt{60}}=1.29$

$P(40\leq x\leq 42)=P(-1.29\leq Z\leq 1.29)$

=0.9016-0.0984=0.803

B)$Z=\frac{40-41 }{6 /\sqrt{60}}=-1.29$

$Pr( \overline{X}<40)=P(Z< -1.29)$

=0.0984

Hence number of sample mean fall below 40 = 0.0984*60= 5.9= 6