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Answer :
The probability that an 18 year old woman selected at random is between 59 and 62 inches tall is 0.5328 or approximately 53.28%.
To solve this problem, we need to use the normal distribution and the formula for calculating probabilities.
First, we need to standardize the values using the formula:
z = (x - mean) / standard deviation
where x is the value we want to find the probability for, in this case, between 59 and 62 inches.
For x = 59 inches:
z = (59 - 61) / 2 = -1
For x = 62 inches:
z = (62 - 61) / 2 = 0.5
Next, we look up the probabilities associated with these z-values using a standard normal distribution table or calculator.
For z = -1, the probability is 0.1587.
For z = 0.5, the probability is 0.6915.
Finally, we subtract the probability of the lower value from the probability of the higher value to find the probability of being between 59 and 62 inches:
P(59 < x < 62) = 0.6915 - 0.1587 = 0.5328
Therefore, the probability that an 18 year old woman selected at random is between 59 and 62 inches tall is 0.5328 or approximately 53.28%.
The heights of 18-year-old women are approximately normally distributed with a mean of 61 inches and a standard deviation of 2 inches. To find the probability that a randomly selected 18-year-old woman is between 59 and 62 inches tall, you would need to use a standard normal distribution table (Z-table) or a calculator with normal distribution functions. The probability would be the area under the curve between 59 and 62 inches.
Learn more about probability at: brainly.com/question/30034780
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