suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. we find the heights of 80 people. (you may need to use the standard normal distribution table. round your answers to the nearest whole number.) (a) how many would you expect to be between 165 and 175 cm tall? 55 correct: your answer is correct. people (b) how many would you expect to be taller than 166 cm?

The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1.

a) To answer this question, we can use the standard normal distribution table to find the proportion of heights that fall within certain ranges of the mean.

The standard normal distribution table gives us the proportion of values within a certain number of standard deviations of the mean.

Since the standard deviation of the heights is 5, we can find the proportion of heights between 165 and 175 cm by looking at the range of values that are one standard deviation below and one standard deviation above the mean.

The mean of the heights is 170, so one standard deviation below the mean is 170 - 5 = 165. One standard deviation above the mean is 170 + 5 = 175. Therefore, the range of heights that are one standard deviation below and one standard deviation above the mean is 165 to 175.

If we look at the standard normal distribution table, we find that approximately 68% of the values fall within one standard deviation of the mean. Since 80 is approximately 68% of 118, we would expect approximately 55 people to have heights between 165 and 175 cm.

Hence, 55 people expect to be between 165 and 175 cm.

b) For the second part of the question, we can find the proportion of heights that are taller than 166 cm by looking at the range of values that are more than one standard deviation above the mean.

The mean of the heights is 170, so more than one standard deviation above the mean is anything greater than 175. If we look at the standard normal distribution table, we find that approximately 95% of the values fall within two standard deviations of the mean.

Since 80 is approximately 95% of 84, we would expect approximately 76 people to be taller than 166 cm.

Hence, 76 people to be taller than 166 cm.

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