The masses of oil palm sold in container have a normal distribution with average of 1,000kg and standard deviation of 35kg. Find the probability that product will weight a) Less than 978kg b) Less than 1,027kg c) Between 978kg and 1,027kg

Question

The masses of oil palm sold in container have a normal distribution with average of 1,000kg and standard deviation of 35kg. Find the probability that product will weight
a) Less than 978kg
b) Less than 1,027kg
c) Between 978kg and 1,027kg

Answer 1

Answer

μ = 1000 k g

σ = 35 k g

a)Find

P (X < 978)

= P (\frac{x - μ}{σ} < \frac{978 - 1000}{35})

= P (z < - 0.629)

P (x < 978) = 0.2647

b)P(x<1027)

P (\frac{x - μ}{σ} < \frac{1027 - 1000}{35})

P = (z < 0.441)

P (x < 1027) = 0.7796

c)

P (978 < x < 1027)

P (\frac{978 - 1000}{35} < \frac{x - μ}{σ} < \frac{1027 - 1000}{35})

P (- 0.629 < z < 0.771)

P (z < 0.771) - P (z < - 0.629)

0.7796 - 0.2647

P (978 < x < 1027) = 0.5149

The masses of oil palm sold in container have a normal distribution with average of 1,000kg and standard deviation of 35kg. Find the probability that product will weight a) Less than 978kg b) Less than 1,027kg c) Between 978kg and 1,027kg

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