STATS ASSIGNMENT

Stats Assignment

Stats Assignment

Question 1

These concerns to the Normal Distribution, and z-scores. I will have to suppose that you have some concept how to use benches of the locality of the distribution. I can't start on a tutorial here.

If P {X1 < 70} = P {X1 > 110} this entails that the community standards 70 and 110 are identical distances either edge of the mean. So the signify should be 90.Usually, you assess a z-value for estimation, and then gaze up the corresponding locality at that z-value. Here, you are granted the locality (0.025) and have to gaze up the z-value which devotes this area.Z-value = (x - µ) / s, so for P{X1 < 70} you will have (70 - 90)/s = - 1.96Hence s = -20 / - 1.96 = 10.2so µ = 90, s = 10.2(of course you could have worked with the top worth, which is on the affirmative edge of the mean.So you would desire the z-value corresponding to an area/probability of (1 - 0.025) = 0.975 (because the areas/probabilities are habitually granted from the left-hand end of the distribution. X1 > 110 mentions to the right-hand follow of the distribution.) The befitting z-value for this locality is +1.96.So, (110 - µ) / s = 1.9620 / s = 1.96, therefore s = 20 / 1.96 = 10.2, as before.)P {X2 < 60} = 0.5 entails that precisely half of the circulation is less than 60, and half is larger than 60, so 60 is the signify value.Therefore P {40 < X2 < 60} = 0.3 entails that P {X2 < 40} = 0.5 - 0.3 = 0.2.The z-value which devotes P {X < z) is -0.842Calculate the z-value: (40 - 60) / s = - 0.842so s = - 20 / -0.8423 = 23.75Hence µ = 60, s = 23.75P {X3 < 10} = P {X3 > 30} Here afresh, the probabilities being identical entails that these X-values are identical distances either edge of the mean. So the signify worth of X3 = (10 + 30)/2 = 20.As in the case of X2, this entails that P{X3 < 20} = 0.5.So P{15 < X3 < 20) = 0.4 entails that 0.4 of the circulation is larger than 15 but less than 20, so 0.1 of the circulation is less than 15; and the z-value corresponding to P{X3 < z} = 0.1 is -1.282Calculating the z-value : z = (15 - 20)/s = -1.282So s = -5/-1.282 = 3.90Hence you have µ = 20, s = 3.90

 

Question 2

Z-score = (value - signify) / sdevRevenue = Enquiries * .05 * 50 = 2.5 * EnquiriesBreakeven income of 5700 / 2.5 = 2280 enquiries. Z = (2280 - 3000)/300 = -2.4Looking up Z = -2.4 on your usual circulation table devotes 0.0082, so there is a 99.18% likelihood of covering costs.Profit goal of 2300 needs income of 8000, which desires 8000/2.5 = 3200 enquiries.Z = (3200 - 3000)/300 = ...