e survey found that men's heights are normally distributed with a mean of 67.2 inches and a standard deviation of 3.1 inches. Jet doorway height of 56.1 inches. "What percentage of men can fit through the door without bending?
To determine the percentage of men who can fit through the door without bending, we need to calculate the proportion of men's heights that are less than or equal to the doorway height.
First, we need to standardize the doorway height by calculating the z-score.
Z = (X - μ) / σ
Z = (56.1 - 67.2) / 3.1
Z = -3.5806
Next, we can use a standard normal distribution table or a statistical software to find the cumulative probability (area under the curve) to the left of the z-score (-3.5806).
Using a standard normal distribution table, the probability is approximately 0.0002.
To convert this probability to a percentage, we multiply by 100:
0.0002 * 100 = 0.02%
Approximately 0.02% of men can fit through the door without bending.
To determine the percentage of men who can fit through the door without bending, we will use the concept of standard deviations in a normal distribution.
Given:
Mean height of men (µ) = 67.2 inches
Standard Deviation (σ) = 3.1 inches
Doorway height (x) = 56.1 inches
To calculate the percentage of men who can fit through the door without bending, we will calculate the z-score, which measures how many standard deviations a value is away from the mean.
z-score = (x - µ) / σ
Calculating the z-score:
z-score = (56.1 - 67.2) / 3.1
z-score = -11.1 / 3.1
z-score ≈ -3.58
Now, we need to find the percentage of men below this z-score using a standard normal distribution table or calculator. The z-score of -3.58 corresponds to an extremely low percentage, close to 0.
Therefore, we can conclude that the percentage of men who can fit through the door without bending is extremely low, close to 0%.