Question

  [ 1+1+1 Marks]

The average number of years, a student takes to complete an advanced diploma is X̅ years. The standard deviation is σ years. Assume the variable is normally distributed. If an individual enrolls in the program, then find the probability that it will take (Use Dataset I to find the value of   ‘ X̅’ and’ σ’),

mean		sd
1	4.4		2.09

a. More than 5.5 years to complete the advance diploma.

b. Less than 4.3 years to complete the advance diploma.

c. Less than 2.8 and more than 4.5 years to complete the advance diploma.

Answer 1

Given = 4.4, = 2.09

To find the probability, we need to find the z scores.

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(a) For P (X > 5.5) = 1 - P (X < 5.5), as the normal tables give us the left tailed probability only.

For P( X < 5.5)

Z = (5.5 – 4.4) / 2.09 = 0.53

The probability for P(X < 5.5) from the normal distribution tables is = 0.7019

Therefore the required probability = 1 – 0.7019 = 0.2981

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(b) For P( X < 4.3)

Z = (4.3 – 4.4) / 2.09 = -0.05

The required probability from the normal distribution tables is = 0.4801

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(c) P(X < 2.8) + P(X > 4.5)

For P( X < 2.8)

Z = (2.8 – 4.4) / 2.09 = -0.77

The probability = 0.2206

P(X > 4.5) = 1 - P(X > 4.5)

Z = (4.5 – 4.4) / 2.09 = 0.05

The Probability for P(X > 4.5) = 1 - 0.5199 = 0.4801

Therefor the required probability = 0.2206 + 0.4801 = 0.7007

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