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Recall that the population average of the heights in the file "pop1.csv" is = 170.035. Using simulations we found that the probability of the sample average of the height falling within 1 centimeter of the population average is approximately equal to 0.626. From the simulations we also got that the standard deviation of the sample average is (approximately) equal to 1.122. In the next 3 questions you are asked to apply the Normal approximation to the distribution of the sample average using this information. The answer may be rounded up to 3 decimal places of the actual value:

1.Using the Normal approximation, the probability that sample average of the heights falls within 1 centimeter of the population average is ______

2.Using the Normal approximation we get that the central region that contains 95% of the distribution of the sample average is of the form 170.035 z 1.122. The value of z is________

3.Using the Normal approximation, the probability that sample average of the heights is less than 168 is________