Question

1. GPAs at CCCOnline are normally distributed with a mean of 2.25 and a standard deviation of 0.46. Find the z-score for a GPA of 3.13.

• 1.087
• 1.804
• 0.8478
• 1.913
• 1.261
• 1.109

2. Adult men have heights with a mean of 69.0 inches and a standard deviation of 8 inches. Find the z-score of a man 76.9 inches tall. (to 2 decimal places)

3. The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 54 and a standard deviation of 10. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 54 and 74?

Answer 1

1) Here

X = 3.13

mean = 2.25

standard deviation = 0.46

$Z = \frac{X-mean}{standard \ deviation} = \frac{3.13-2.25}{0.46} = 1.913$

2)

X = 76.9

mean = 69.0

standard deviation = 8

$Z = \frac{X-mean}{standard \ deviation} = \frac{76.9-69}{8} = 0.9875$

3)

$\bar x= 54 \\ \\ \sigma = 10$

Required propability

= P( 54 < X < 74)

$P(\frac{54-54}{10} < Z < \frac{74-54}{10} ) = P(0< Z < 2) = 0.47$'

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