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Answer :
The probability that a randomly chosen 15-to-20-year-old male from Turkey has a height of more than 190 cm is approximately 0.0228.
To find this probability, we first need to standardize the height of 190 cm using the given mean and standard deviation. This is done by calculating the z-score:
z = (X - μ) / σ
Where:
- X is the value we're interested in (190 cm in this case)
- μ is the mean (178 cm)
- σ is the standard deviation (5 cm)
z = (190 - 178) / 5 = 2.4
Next, we look up this z-score in the standard normal distribution table, which gives us the probability associated with a z-score of 2.4. The probability for a z-score of 2.4 is approximately 0.9914.
However, we are interested in the probability of heights *more than* 190 cm, which is the area under the normal distribution curve to the right of the z-score. Since the total area under the curve is 1, we subtract the probability we found from 1 to get the final probability:
Probability = 1 - 0.9914 = 0.0086
So, the probability that a randomly chosen 15-to-20-year-old male from Turkey has a height of more than 190 cm using the standard normal distribution table is approximately 0.0086.
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