Question

Suppose that an airline uses a seat width of 17.4 in. Assume men have hip breadths that are normally distributed with a mean of 14.9 in. and a standard deviation of 1 in. Complete parts​ (a) through​ (c) below.

​(a) Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 17.4 in. The probability is ________. ​(Round to four decimal places as​ needed.)

​(b) If a plane is filled with 120 randomly selected​ men, find the probability that these men have a mean hip breadth greater than 17.4 in. The probability is ______ ​(Round to four decimal places as​ needed.) ​

(c) Which result should be considered for any changes in seat​ design: the result from part​ (a) or part​ (b)?

The result from ▼ part (b) OR part (a) should be considered because ▼ only average individuals should be considered OR the seats are occupied by individuals rather than means.

Answer 1

µ = 14.9, σ = 1

a) P(X > 17.4) =

= P( (X-µ)/σ > (17.4-14.9)/1)

= P(z > 2.5)

= 1 - P(z < 2.5)

Using excel function:

= 1 - NORM.S.DIST(2.5, 1)

= 0.0062

b)

µ = 14.9, σ = 1, n = 120

P(X̅ > 17.4) =

= P( (X̅-μ)/(σ/√n) > (17.4-14.9)/(1/√120) )

= P(z > 27.3861)

= 1 - P(z < 27.3861)

Using excel function:

= 1 - NORM.S.DIST(27.3861, 1)

= 0.0000

c) The result from part (b) should be considered because only average individuals should be considered.