Answer to Question #207340 in Statistics and Probability for Redangel

Question

The weights of 500 students are normally distributed with a mean of 46 with standard deviation of 2 kg

a. Draw a normal curve distribution with 2-scores and equivalent raw scores. kg

b. What percent of all the students weighs below 42 kg?

c. If a student from this group is randomly selected, what is the probability that he/she weighs between 46 kg and 48 kg?

d. How many students in the given group are heavie

Answer 1

$n=500 \\ \mu=46 \\ \sigma= 2$

a.

$x= \mu +Z \times \sigma \\ Z=2 \\ x = 46 + 2 \times 2 = 50$

b.

$P(X<42) =P(Z< \frac{42-46}{2}) \\ = P(Z< -2) \\ = 0.0227 \\ = 2.27 \; \%$

c.

$P(46<X<48) = P(X<48) -P(X<46) \\ = P(Z< \frac{48-46}{2}) -P(Z< \frac{46-46}{2}) \\ = P(Z< 1) -P(Z< 0) \\ = 0.8413 -0.5 \\ = 0.3413$

d. Incomplete problem.