Women have head circumferences that are normally distributed with a mean given by u =24.24 in., and a standard deviation given by σ=1.1 in. complete parts a through c below. {i only need the 2 answers to question c }a) if a hat company produces women's hats so that they fit head circumferences between 24.0 in. and 25 in., what is the probability that a randomly selected woman will be able to fit into one of these hats? = 0.3420b) b. if the company wants to produce hats to fit all women except for those with the smallest 1.5% and the largest 1.5% head circumferences, what head circumferences should be accommodated? =minimum=21.85 maximum= 26.63c) if 6 women are randomly selected, what is the probability that their mean head circumference is between 24.0 in. and 25.0 in.? (round to 4 decimal places)if this probability is high, does it suggest that an order of 6 hats will very likely fit each of 6 randomly selected women? why or why not? (assume that the hat company produces women's hats so that they fit head circumferences between 24.0 in. and 25.0 in.)

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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