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.

   Bags of rice average 500 g, with standard deviation 30 g. Luz averages samples of 100. What is the standard deviation of the sample mean, in g?

   3
5. 5.

   Phone batteries last a mean of 40 hours (standard deviation 12). A sample of 36 averages 43 hours. Milo compares it with the balance point. What is the z-score of this sample mean?

   1.5
6. 6.

   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
7. 7.

   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
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