Answer:
There is a significant difference between the two proportions.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for difference between population proportions is:

Compute the sample proportions as follows:

The critical value of <em>z</em> for 90% confidence interval is:

Compute a 90% confidence interval for the difference between the proportions of women in these two fields of engineering as follows:


There will be no difference between the two proportions if the 90% confidence interval consists of 0.
But the 90% confidence interval does not consists of 0.
Thus, there is a significant difference between the two proportions.
Solution :
Given data :
The mean length of the steel rod = 29 centimeter (cm)
The standard deviation of a normally distributed lengths of rods = 0.07 centimeter (cm)
a). We are required to find the proportion of rod that have a length of less than 28.9 centimeter (cm).
Therefore, P(x < 28.9) = P(z < (28.9-29) / 0.07)
= P(z < -1.42)
= 0.0778
b). Any rods which is shorter than
cm or longer than
cm that re discarded.
Therefore,
P (x < 24.84 or 25.16 < x) = P( -59.42 < z or -54.85)
= 1.052
Sin 45 = 62.5/h
h = 62.5 / sin 45
h = 88.3 cm