Question

9. Suppose that the average festival attendee spends $1100 for the entire Coachella experience with standard deviation of about $40. Also suppose that the total expenditure is approximately normally distributed. What is the probability that a random festival attendee will spend between $1105 and $1200 on the Coachella experience? a. on the Coadheila sperien People whose total expenditure is in the lowest 196 are considered cheap. You don't want to be lame and considered cheap but you can only afford to spend $975 on the C experience. Are you considered cheap? Explain. b. oachella 10. Determine the values of two z-scores that separate the middle 80% from the outside 20%. (Hint: Draw a picturel)

Answer 1

Answer# 9)
Mean ( M ) = 1100

Standard deviation ( S ) = 40

.

part a)

P(1105 < x < 1200) = P(x < 1200) - P(x < 1105)

Formula of Z is:

Z =( x - M ) / S

.

Z1 = ( 1200-1100) /40

Z1 = 2.5

P(x < 1200) = P(z < 2.5) = 0.9938

.

Z2 = (1105-1100) /40

Z2 = 0.125

P(x < 1105) = P(z < 0.125) = 0.5497

P(1105 < x < 1200) = 0.9938 -0.5497

P(1105 < x < 1200) = 0.4441

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Part b)

P(x < 975)

Z = (975 -1100)/40

Z = -3.125

P(z < -3.125) = 0.000889 ~ 0.0889%

Since the percent of $975 is less than 1% , it would be considered as cheap