Probabilities and percentiles

Suppose the weights of students follow a normal distribution with μ = 47 kg and σ = 4 kg. What is the probability that a randomly selected student is less than 50 kg?

• 77.34%

• 99.38%

• 50%

• 75%

Suppose the heights of students follow a normal distribution with μ = 170 cm and σ = 10 cm. What is the probability that a randomly selected student is higher than 180 cm?

• 70%

• 15.87%

• 84.13

• 30%

Find the 75th percentile in a normal distribution where μ = 50 and σ = 5.

• A score of 35.35 or approximately 35 marks the top 25% of the distribution.

• A score of 35.53 or approximately 36 marks the top 25% of the distribution.

• A score of 53.35 or approximately 53 marks the top 25% of the distribution.

• A score of 53.53 or approximately 54 marks the top 25% of the distribution.

Find the 85th percentile in a normal distribution where μ = 50 and σ = 5.

• A score of 52.2 or approximately 52 marks the top 15% of the distribution.

• A score of 53.2 or approximately 53 marks the top 15% of the distribution.

• A score of 54.2 or approximately 54 marks the top 15% of the distribution.

• A score of 55.2 or approximately 55 marks the top 15% of the distribution.

Finding probabilities using the Standard Normal Table.

P(Z < -1.53) = _____.

• 3.6%

• 3.9%

• 6.3%

• 9.3%

Finding probabilities using the Standard Normal Table.

P(Z < 2.89) = _____.

• 98.18%

• 98.81%

• 99.18%

• 99.81%

Determining z-scores for given percentiles.

60^th percentile         z = _____.

• 0.25

• 0.52

• 2.05

• 2.50

Determining z-scores for given percentiles.

80^th percentile         z = _____.

• 0.38

• 0.48

• 0.84

• 0.94

Converting z-scores back to raw scores.

If z = 1.25, μ = 60 and σ = 6, then x = ____.

• 67.5

• 65.7

• 57.6

• 56.7

Converting z-scores back to raw scores.

z = - 0.35, μ = 70 and σ = 5, then x = ____.

• 28.65

• 28.56

• 68.25

• 68.52