7) Data from a small bookstore are shown in the accompanying table. The manager wants to predict Sales from Number of Sales People Working. Number of sales people working | Sales (in $1000) | 4 | 12 | 5 | 13 | 8 | 15 | 10 | 16 | 12 | 20 | 12 | 22 | 14 | 22 | 16 | 25 | 18 | 25 | 20 | 28 | x=11.9 | y=19.8 | SD(x)=5.30 | SD(y)=5.53 |

a) Find the slope estimate, b1. Use technology or the formula below to find the slope. b1=rsysx Enter x,y Data in TI-84 under STAT > STAT > CALC > 8: LinReg(a+bx) b1=1.023 b) What does b1 mean, in this context?
The slope tells how the response variable hanges for a one unit step in the predictor
Thus, an additional; $1,023 of sales associated with each additional sales
E(X) = ∑x ∙ P(x) = 0(0.3) +1(0.3) +2(0.4) = 1.1 There, the expected value of the number of night potential customers will need is 1.1
b) Find the standard deviation of the number of nights potential customers will need.
The standard deviation is the square root of the variance.
First, Find the Variance: To do so, find the deviation of each value of X from the mean and square each deviation. The variance is the expected value of these squared deviations and is found using the formula below. σ² = Var(X) = ∑(x - µ)²P(x)
Find the deviation for each value of X. Remember that E(x)=1.1

Vacation Package | Nights Included | Probability P(X=x) | Deviation (x – E(X)) | Day Plan | 0 | 30100=0.3 | 0 – 1.1 = -1.1 | Overnight Plan | 1 | 30100=0.3 | 1 – 1.1 = -0.1 | Weekend Plan | 2 | 40100=0.4 | 2 – 1.1 = 0.9 |

Now find the variance using the formula σ²=Var(X)=∑(x - µ)²P(x)
Var(X) = ∑(x - µ)²P(x) = (-1.1)²(0.3) + (-0.1)²(0.3) + (0.9)²(0.4) = 0.69

Finally, the standard deviation also known as σ is the square root of the variance.
Σ = Var(x) = 0.69 = 0.83
Therefore, the standard deviation of the number of nights potential customers will need is approximately 0.83 nights.

17) A grocery supplier believes that in a dozen eggs, the mean number of broken eggs is 0.2 with a standard deviation of 0.1 eggs. You buy 3 dozen eggs without checking them.
a) How many broken eggs do you get?
The expected value of