Suppose the heights of the students of NSU are normally distributed with a mean of 167 cm and a standard deviation of 6 cm. (a) What is the probability that a randomly selected student will be taller than 175 cm? (b) What is the probability that the height of a randomly selected student will lie between 160 cm and 180 cm? (c) Find the height below which 10% of the heights of the students fall. (d) What is the probability that the mean height of 36 selected students will lie between 165 cm and 175 cm? (e) If the mean height of 36 selected students is 165 cm, find the 98% confidence interval of the true mean height. What is the margin of error in this case? (f) How large a sample should be selected to be 90% confident that the estimate of the average height of the students will be within 1 cm of the true average height?
Added by Juan Carlos R.
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We can use the standard normal distribution to find this probability. z = (175 - 167) / 6 = 1.33 Using a standard normal distribution table or calculator, we find that the probability of a randomly selected student being taller than 175 cm is approximately Show more…
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