z-scores and normal probabilities

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   z-table (area to the left): z = 1.20: 0.8849. Scores on Ari's school puzzle test are normal with mean 100 and SD 15. To four decimal places, what fraction of the scores are above 118?

   0.1151
2. 2.

   z-table (area to the left): z = 1.50: 0.9332. Times for Bo's class to solve a riddle are normal with mean 50 s and SD 6 s. To four decimal places, what fraction of the times are below 41 s?

   0.0668
3. 3.

   z-table (area to the left): z = 2.25: 0.9878. Battery hours for the flashlights in Jun's class are normal with mean 8 and SD 0.4. To four decimal places, what fraction of the battery times are below 7.1 hours?

   0.0122
4. 4.

   Kira scores 82 on a math quiz (mean 70, SD 6) and 90 on a spelling quiz (mean 85, SD 5). Which result is better compared with its own group?

   • The math quiz: z = 2, against z = 1
   • They are equal: both are above the mean
   • The spelling quiz: 90 is the larger number
5. 5.

   Luz scores 78 on Test A (mean 72, SD 3) and 88 on Test B (mean 80, SD 8). Which result is better compared with its own group?

   • They are equal: both are above the mean
   • Test A: z = 2, against z = 1
   • Test B: 88 is the larger number
   • Test B: 8 above its mean, more than 6
6. 6.

   Milo reads 45 pages (class mean 30, SD 5) and writes 40 lines (class mean 32, SD 2). Which result is better compared with its own group?

   • They are equal: both are above the mean
   • The reading: 15 above its mean, more than 8
   • The reading: 45 is the larger number
   • The writing: z = 4, against z = 3
7. 7.

   Noah's bean plant is 64 cm (class mean 60, SD 2) and sunflower is 70 inches (class mean 61, SD 6). Which result is better compared with its own group?

   • The bean plant: z = 2, against z = 1.5
   • The sunflower: 9 above its mean, more than 4
   • The sunflower: 70 is the larger number
   • They are equal: both are above the mean
8. 8.

   z-table (area to the left): z = 1.00: 0.8413; z = 1.50: 0.9332. Puzzle times in Pia's class are normal with mean 50 s and SD 10 s. To four decimal places, what fraction of the times are between 40 and 65 s?

   0.7745
9. 9.

   z-table (area to the left): z = 1.50: 0.9332. Long jumps in Tala's class are normal with mean 12 feet and SD 2 feet. To four decimal places, what fraction of the jumps are between 9 and 15 feet?

   0.8664
10. 10.

    z-table (area to the left): z = 1.40: 0.9192; z = 1.80: 0.9641. Apple weights at Ari's farm visit are normal with mean 80 g and SD 5 g. To four decimal places, what fraction of the weights are between 71 and 87 g?

    0.8833