The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16. Determine the interval of 95% confidence for the average heights of the population. With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the heights to be less than 2 cm from the sample mean?

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The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of
the population are random variables that follow a normal distribution with a variance of 0.16. Determine the
interval of 95% confidence for the average heights of the population. With a confidence level of 90%, what
would the minimum sample size need to be in order for the true mean of the heights to be less than 2 cm
from the sample mean?

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