Binomial averages, the Central Limit Theorem and the normal curve

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Phone batteries last a mean of 40 hours, with standard deviation 12 hours. Esme averages samples of 36. What is the standard deviation of the sample mean, in hours?

   2
2. 2.

   Sunflowers in a field average 150 cm tall, with standard deviation 20 cm. Jun averages samples of 25. What is the standard deviation of the sample mean, in cm?

   4
3. 3.

   Bus waits average 12 minutes, with standard deviation 6 minutes. Kira averages samples of 16. What is the standard deviation of the sample mean, in minutes?

   1.5
4. 4.

   Sunflowers average 150 cm (standard deviation 20). A sample of 25 averages 142 cm. Ren compares it with the balance point. What is the z-score of this sample mean?

   -2
5. 5.

   Bus waits average 12 minutes (standard deviation 6). A sample of 16 waits averages 15 minutes. Tala compares it with the balance point. What is the z-score of this sample mean?

   2
6. 6.

   Rice bags average 500 g (standard deviation 30). A sample of 100 bags averages 494 g. Zee compares it with the balance point. What is the z-score of this sample mean?

   -2
7. 7.

   Ari flips a fair coin 100 times and gets 60 heads. With n = 100 and p = 0.5, and the normal curve for the count, what is the z-score of 60?

   2
8. 8.

   Bo's class flips 400 coins and gets 190 heads. With n = 400 and p = 0.5, and the normal curve for the count, what is the z-score of 190?

   -1
9. 9.

   In 625 spins of a red-and-blue spinner, Esme gets 135 reds. With n = 625 and p = 0.2, and the normal curve for the count, what is the z-score of 135?

   1
10. 10.

    Jun's school flips 900 coins and gets 495 heads. With n = 900 and p = 0.5, and the normal curve for the count, what is the z-score of 495?

    3