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Please show carefully detailed work, including how the areas under the normal curve were found and calculated.

Assume that the distribution of age in the population is approximately normal with a mean of 34.7 years and a standard deviation of 3.4 years. Find the following probabilities/percentiles

i) P (Age ≥ 40)

ii) P (30 ≤ Age ≤ 40)

iii) P (Age ≤ 30)

iv) Age that corresponds to the 90th percentile

v) Age that corresponds to the 25th percentile

vi) Age that corresponds above the 25th percentile

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