Use the information stated below to complete the following problems. Show all wo

Question

Use the information stated below to complete the following problems. Show all work, use the correct notation and include a sketch of the m=normal curve , shaded to match each problem. If you use Statcruch, make sure the curve is labeled correctly with the 68-95-99.7% values. Round probabilities to 4 places and percents too 1 decimal place. Write a conclusion too the context of the original problem. Don't forget to use "approximately" in the conclusion.

You can use the z-formula and Table A-2 to calculate these problems by hand OR you can use calculators or Statcrunch. It is always good to know how to do these problems by hand, but it is not required.

Assume that the distribution of the number of chocolate chips in Chips Ahoy regular cookies is approximately normal with a mean of 24.0 chocolate chips and a standard deviation of 2.6 chocolate chips. N(24.0, 2.6)

a) What percent of cookies contain at least 22 chocolate chips?

b) What percentage of Chips Ahoy cookies has more than 27 chips?

c) What percentage of Chips Ahoy cookies have between 23 and 26 chips?

d) If 25 cookies are randomly selected, find the probability that the mean number of chips is less than 25. Convert the probability to a percent for the conclusion.

e) What is the number of chocolate chips at the 75% level?

Explanation / Answer

a)

percent of cookies contain at least 22 chocolate chips:

~ 77.91%

b)

~12.43%

c)percentage of Chips Ahoy cookies have between 23 and 26 chips

d)

d)

at 75% ; z =0.6745

hence corresponding cookies =mean +z*std deviaiton=24+0.6745*2.6=25.75

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