A hot dog vendor at Wrigley Field sells hot dogs for $1.50 each. He buys them for $1.20 each. All the hot dogs he fails to sell at Wrigley Field during the afternoon can be sold that evening at Comiskey Park for $1 each. The daily demand for hot dogs at Wrigley Field is normally distributed with a mean of 40 and a standard deviation of 10.a. If the vendor buys hot dogs once a day, how many should he buy?b. If he buys 52 hot dogs, what is the probability that he will meet all of the day’s demand for hot dogs at Wrigley?

43 ; 0.88493

Step-by-step explanation:

Using the Zscore formula :

Zscore = (x - m) / s

m = mean ; s = standard deviation

Profit = $1.5 - $1.2 = $0.3

Loss = $1.2 - $1 = 0.2

Cummlative probability :

Profit / (profit + loss)

0.3 / (0.3 + 0.2) = 0.3 / 0.5 = 0.6

To obtain the x, at Z at 0.6 = 0.26

m = 40 ; s= 10

Hence,

0.26 = (x - 40) / 10

0.26 * 10 = x - 40

2.6 = x - 40

2.6 + 40 = x

x = 42.6 `; 43 approximately

Probability of meeting day's demand at Wrigley

x = 52

P(x < 52) :

Zscore = (52 - 40) / 10

P(Z < 1.2)

Z = 0.88493

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: