Question

In the data set ( joined file), Use the July#Sales ( column F) variable for this exercise. Suppose someone claims the population mean is 23, and the standard deviation is 4.5

PART 1 - For now, you assume both of the claims about the population are correct.

1a. Given the assumed pop. mean and st.dev, calculate the probability of observing a value above the number for your first data point in your file.
1b. Suppose you collected 8 new data points in a new sample. Calculate the probability that the mean of these 8 new data points is above the number for your first data point in your file.
1c. If this is a normally distributed variable, above what value should you find 70% of data points? How many of the values from your data set are above this value?
1d. If this is a normally distributed variable, between what two numbers (centered around the assumed mean) should you find 68% of data points? What percentage of your data points are between these numbers?
1e. Think about your answers to 1c and 1d. Does this variable appear to be normally distributed with this mean and standard deviation?

1 AssociatelDJuneCustom June#Sales June$Sales JulyCustomers July#Sales 2 005 3 006 4 008 5 010 6 012 7 013 8 014 9 018 10 020 11 022 12 026 13 027 14 030 15 034 16 035 17 037 18 040 19 042 20 044 21 045 22 052 23 056 24 057 25 059 26 062 27 063 28 070 29 071 0 072 July$Sales Region JuneTraining 27646 33240 25410 33580 16427 29732 44708 29110 15332 14902 21188 10558 9570 31182 30434 18276 41840 25580 41310 13000 24760 52240 S 60974 S 24065 W 27680 N 36652 S 19070 N 18660 S 42034 N 19856 W 28635 S 11450 W 37195 S 25272 W 20902 S 40131 N 43535 W 44916 N 50130 S 14332 S 23308 E 26170 W 31958 S 25088 N 4319 S 22205 S 26365 W 36326 W 48841 W 33828 E 18 39 13 19 13 12 10 39 27 12 49 10 18 21 15 31476 37051 12951 19640 34886 49957 17390 38 25 18 27 39 28 10 49 NNYYYYYYNYYYYYYYYYYYYNYNY ESNSNNN 800089350055080068 238117077275712315 8115460 1259757 33732 3322213124334633223162421 1455631745176600610275407 3221113112212322122132211 9968189558739226345221579 4332433223332424334354521 06167666050568410 838720735417972 321 7313338 132231 193325137768812 459227511312646 112523122 213 0836919405456823402669751 11211 1222221 2 8373464517218289010869612 2223233323242222343223132 5689012379 8888999999 2581 123690 111-12 0123456789 567890123 444445555 2 C0 Evaluations of Sales Associates at an Industrial Machinery Wholesaler AssociatelD Sales associate's company identification number JuneCustomers Number of customers associate met with during June June#Sales-Number of sales placed by associate during June JuneSSales Total amount, in dollars, of associate's sales during June JulyCustomers Number of customers associate met with during July July#Sales = Number of sales placed by associate during July JulySSales Total amount, in dollars, of associate's sales during July Region Location of Employee's Store: North, South, East, or West JuneTraining Whether or not associate completed a sales training program at the end of June

Answer 1

a)

4.5 μ = 23, σ P(X > 32) =? X- 11 32-23 . P(z > 2) = 0.02275

b)

μ 23, σ 4.5, n = 8 P(X > 32) =? P(X > 32) = P(X-μ > 32-23) P(z > 5.65) = 0 一,1 ..

c)

11 23.ơ 4.5 P(X > x1) = 0.70.2.1 =? We know from standard normal table P(Z >-0.5244) = 0.70 1 -23 4.50.5244 r10.5244 * 4.52320.6402

So above 20.64, we will have 70% of the data.

We have 31 data points above this value, which is 57.4 %

d)

P(z! < X < x2) = 0.68,T1,T2 =? We know from standard normal table -0.9945 < Z < 0.9945) = 0.68 -23 =-0.9945 45 0.9945 ri =ー0.9945 * 4.5 T2 - 23 23-18.525 2 0.9945 4.5 r2 0.9945 * 4.5 + 23 = 27.475

We have 25 data points within this interval in our data set, which is 46.29%

e)

Given our values in the above two parts and the proportion of values that are in those intervals, its seems hard to believe that the data follows a normal distribution.

Below is the data of July $sales.

July$Sales
10
10
12
13
13
13
14
14
14
15
15
16
16
16
17
17
17
17
20
20
20
20
21
21
21
21
22
22
23
24
24
25
25
25
25
25
25
26
26
26
26
27
27
29
29
29
31
31
32
35
36
36
37