Question

18, Steel rods are manufactured with a mean length of 26 centimeter​ (cm). Because of variability in the manufacturing​ process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Complete parts ​(a) to ​(d).

​(a) What proportion of rods has a length less than 25..9 ​cm?

nothing ​(Round to four decimal places as​ needed.)

​(b) Any rods that are shorter than 25.87 cm or longer than 26.13 cm are discarded. What proportion of rods will be​ discarded?

nothing ​(Round to four decimal places as​ needed.)____​(Round to four decimal places as​ needed.)

​(c) Using the results of part ​(b)​, if 5000 rods are manufactured in a​ day, how many should the plant manager expect to​ discard?

____​(Use the answer from part b to find this answer. Round to the nearest integer as​ needed.)

​(d) If an order comes in for 10,000 steel​ rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 25.9 cm and 26.1 cm?

___ ​(Round up to the nearest​ integer.)

19, According to a​ study, 59​% of all males between the ages of 18 and 24 live at home. ​ (Unmarried college students living in a dorm are counted as living at​ home.) Suppose that a survey is administered and 163 of 248 respondents indicated that they live at home.​ (a) Use the normal approximation to the binomial to approximate the probability that at least 163 respondents live at home.​ (b) Do the results from part​ (a) contradict the​ study?

​(a) ​P(X≥163​)=___​(Round to four decimal places as​ needed.)

​(b) Does the result from part​ (a) contradict the results of the​ study?

A.

Yes​, because the probability of ​P(X≥163​) is greater than 0.05 .

B.

Yes​, because the probability of ​P(X≥163​) is less than 0.05

C.

No, because the probability of ​P(X≥163​) is less than 0.05 .

D.

No​, because the probability of ​P(X≥163​) is greater than 0.05

8, Suppose the monthly charges for cell phone plans are normally distributed with mean μ=$67 and standard deviation σ=​$16

​(a) Draw a normal curve with the parameters labeled. ​(b) Shade the region that represents the proportion of plans that charge less than ​$51. ​(c) Suppose the area under the normal curve to the left of X=​$51 is 0.1587. Provide an interpretation of this result.

please answear all questions

Answer 1