Complete Question:
Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15
Answer:
0.14
Step-by-step explanation:
Given that :
Expected value = 0.47
Standard deviation = 0.15
Sample size, n = 30
The mean = expected value * sample size
Mean = 0.47 * 30 = 14.1
Standard deviation of sample = σ / √n
0.15 = σ/√30
σ = 0.8216
P(x > 15) :
Z = (x - mean) /standard deviation
Z = (15 - 14.1) / 0.8216 = 1.095
P(Z > 1.095) = 0.1367
P(Z > 1.095) = 0.14
