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 = 1.60: 0.9452. Heights of the sunflowers in Esme's garden are normal with mean 65 inches and SD 5 inches. To four decimal places, what fraction of the heights are above 73 inches?

   0.0548
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 spelling quiz: 90 is the larger number
   • The math quiz: z = 2, against z = 1
   • They are equal: both are above the mean
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 B: 88 is the larger number
   • Test A: z = 2, against z = 1
   • 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?

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

   • They are equal: both are above the mean
   • 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
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