Respuesta :
Answer:
a: 0.1%
b. No it does not
c. Probably for safety reasons
Step-by-step explanation:
for women: z = (55.9 - 63.9)/3.6 = -2.22
The p-value for z = -2.22 is 0.0132, so only 1.32% of women could walk through without bending
for men: z = (55.9 - 69.7)/3.6 = -3.83
The p-value for z = -3.83 is 0.001, so only 0.1% of men could walk through without bending
Using the normal distribution, it is found that:
a) The percentage of men who can fit without bending is 0.02%.
b) A very small percentage of people can fit through the door, thus the dimensions are not adequate. Possible, the engineers did not design a large door because of engineering constraints.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations the measure is from the mean.
- After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
Item a:
- Men have mean of 69.7 in, thus [tex]\mu = 69.7[/tex]
- Standard deviation of 3.6 in, thus [tex]\sigma = 3.6[/tex]
The proportion is the p-value of Z when X = 55.9, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.9 - 69.7}{3.6}[/tex]
[tex]Z = -3.83[/tex]
[tex]Z = -3.8[/tex] has a p-value of 0.0002.
0.0002 x 100% = 0.02%
The percentage of men who can fit without bending is 0.02%.
Item b:
A very small percentage of people can fit through the door, thus the dimensions are not adequate. Possible, the engineers did not design a large door because of engineering constraints.
A similar problem is given at https://brainly.com/question/12476124
