Weights of women in one age group are normally distributed with a standard deviation sigma of 20 lb. a researcher wishes to estimate the mean weight of all women in this age group. find how large a sample must be drawn in order to be 90% confident that the sample mean will not differ from the population mean by more than 3.5 lb.

88.344 or Rounding up to 89

Step-by-step explanation:

When talking about the confidence level, we need to find the z-score for 90% confidence. Since z-scores are constant values we can easily find these online. In this case the z-score for 90% confidence is z = 1.64485

The formula for z-score is as follow

Where

Now we know from the question that

We can easily solve the above equation to find the Standard Deviation

To find Population Size

-10i^2-4i

step-by-step explanation:

evaluate for p=2,q=5i

(2−4)(2+5i)i

(2−4)(2+5i)i

=−10i2−4i

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.