Answer to Question #173860 in Statistics and Probability for Rustom

Question

In a Science test, the mean score is 42 and the standard deviation is 5. Assuming the scores are normally distributed, what is the probability that the score is:

B. less than 50?

1. Convert the raw score of 50 to a z-score.

2. Draw the normal curve and locate the given z-value or values at the base line of the curve. Then, draw a verticalline through the given z-value or values and shade the required region.

3. Use the table and find the area that corresponds to the computed z-score.

4. Examine the shaded region and make an appropriate operation to apply, if needed

5. Make a concluding statement.

Answer 1

We have that:

$\mu=42$

$\sigma=5$

$P(X<50)=P(Z<\frac{x-\mu}{\sigma})$

$Z=\frac{x-\mu}{\sigma}=\frac{50-42}{5}=1.6$

$P(X<50)=P(Z<1.6)=0.9452$

In a Science test the probability that the score is less than 50 is 94.52%