The height of women are normally distributed with a mean of 66 inches and a standard deviation of 2.6 inches. Use a graphing calculator to find the probability that a woman chosen at random will be taller than 70 inches.
To find the probability that a woman chosen at random will be taller than 70 inches, we need to calculate the z-score corresponding to 70 inches and then use a standard normal distribution table or graphing calculator to find the corresponding probability.
The z-score is calculated as:
z = (x - μ) / σ
z = (70 - 66) / 2.6
z = 1.54
Now, using a graphing calculator or a standard normal distribution table, we can find the probability that a woman chosen at random will be taller than 70 inches by finding the area to the right of the z-score of 1.54.
Using a graphing calculator and the standard normal distribution function, we can input the z-score of 1.54 and find that the probability is approximately 0.0594.
Therefore, the probability that a woman chosen at random will be taller than 70 inches is approximately 0.0594 or 5.94%.