Question

Use the z-table provided and answer the following questions.

41. What is the proportion of scores greater than z = 1.15?

42. What is the proportion of scores less than z = 1.73?

43. What is the proportion of scores greater than z = -0.90?

44. What is the proportion of scores between z = -1.04 and z = 1.39?

45. What is the proportion of scores between z = 1.08 and z = 1.21?

46. If the proportion of scores less than z is 0.1587, what is z?

47. If the proportion of scores greater than z is 0.7734, what is z?

48. If the proportion of scores greater than z is 0.0052, what is z?

49. If the proportion of scores less than z is .0179, what is z?

50. If the proportion of scores between -z and +z is 0.2812, what is z?

Answer 1

Solution :

Using standard normal table,

41.

P(z > 1.15) = 1 - P(z < 1.15) = 1 - 0.8749 = 0.1251

proportion = 0.1251

42.

P(z < 1.73) = 0.9582

proportion = 0.9582

43.

P(z > -0.90) = 1 - P(z < -0.90) = 1 - 0.1841 = 0.8159

proportion = 0.8159

44.

P(-1.04 < z < 1.39)

= P(z < 1.39) - P(z < -1.04)

= 0.9177 - 0.1492

= 0.7685

proportion = 0.7685

45.

P(1.08 < z < 1.21)

= P(z < 1.21) - P(z < 1.08)

= 0.8869 - 0.8599

= 0.027

proportion = 0.027

46.

P(Z < z) = 0.1587

P(Z < -1.00) = 0.1587

z = -1.00

47.

P(Z > z) = 0.7734

1 - P(Z < z) = 0.7734

P(Z < z) = 1 - 0.7734

P(Z < -0.75) = 0.2266

z = -0.75

48.

P(Z > z) = 0.0052

1 - P(Z < z) = 0.0052

P(Z < z) = 1 - 0.0052

P(Z < 2.56) = 0.9948

z = 2.56

49.

P(Z < z) = 0.0179

P(Z < -2.10) = 0.0179

z = -2.10

50.

P(-z < Z < z) = 0.2812

P(Z < z) - P(Z < -z) = 0.2812

2P(Z < z) - 1 = 0.2812

2P(Z < z) = 1 + 0.2812 = 1.2812

P(Z < z) = 1.2812 / 2 = 0.6406

P(Z < 0.36) = 0.6406

z = 0.36