Clear explaination and working please Question 3 (20 Marks) Suppose the number o

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Clear explaination and working please

Question 3 (20 Marks) Suppose the number of ice cream cones that a store sells daily in summer is normally distributed with a mean of 250 cones and a standard deviation of 20 cones. Calculate the following values. Show all steps in your answers. (a) Find the probability that the number of cones sold is greater than 280. (5 Marks) (b) Find the probability that the number of cones sold is less than 210. (5 Marks) ()Find the probability that the number of cones sold is greater than 230 and less than 270. (5 Marks) d) The management will revise the marketing strategy if sales drop into the bottom 25% of the distribution. What is the minimum number of sales required before the marketing strategy requires revision? (5 Marks)

Explanation / Answer

Solution:- Given that mean = 250,sd = 20

a) P(X > 280) = P(Z > (X - mu)/sd)
= P(Z > (280 - 250)/20)
= P(Z > 1.5)
= 0.0668

b) P(X < 210) = P(Z < (X - mu)/sd)
= P(Z < (210 - 250)/20)
= P(Z < -2)
= 0.0228

c)P(230 < X < 270) = P((230 - 250)/20 < Z < (270 - 250)/20)
= p(-1 < Z < 1)
= 0.6826

d)P(Z < (x - mu)/sd) = 0.25
x = mu - sd(0.675)
x = 250 -20(0.675)
x = 236.5

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