Question

Help needed stat hw

Show work and make sure to include the appropriate probability statements [Ex. P(AB), PIX = 15), P(35 X<5), etc.) for probability problems Delivery time for a Restaurant follows a normal distribution with a mean of 20 minutes and a standard deviation of 6.44 minutes. Answer the following questions: (a) The Restaurant advertises that if the food is not delivered within half an hour then it is free. Suppose that you just placed an order. What is the probability that your food will be free due to late delivery? (b) What is the probability that the food delivery will take between 15 mins and 27 minutes? (c) The Restaurant realized that the 30-minute rule resulted in too much free food. So, they decided to revise their policy so that only 1% of the food will end up being free of charge due to delivery delay. What should the new cutoff time be?

Answer 1

Mean = u = 20

Std. dev = s = 6.44

(a) half a hour = 30 minutes

P( X > 30 ) = ?

Z-score = ( x - u)/s

Z(30) = (30-20)/6.44 = 1.5528

P( X > 30 ) = P ( Z > 1.5528 ) = 0.0602

• Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals) Specify Parameters: Mean 0 SD 1 Above 1.5528 Below Between Outside and Results: Area (probability) 0.0602

(b)

P ( 15 < X < 27 )

Z(15) = (15 - 20)/6.44 = -0.7764

Z(27) =(27-20)/6.44 = 1.0870

P ( 15 < X < 27 ) = P( -0.7764 < Z < 1.0870 ) = 0.6427

• Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals) Specify Parameters: Mean 0 SD 1 Above Below • Between -0.7764 Outside and 1.0870 and Results: Area (probability) 0.6427

(c) Top 1% => 99th percentile

z score corresponds to the 99th percentile = > 2.326

2.326 = ( x - 20)/6.44

x = 2.326*6.44 + 20

X = 34.9794 = 34.98 minutes

Area from a value (Use to compute p from Z) • Value from an area (Use to compute Z for confidence intervals) Specify Parameters: Area 0.01 Mean 0 SD 1 Results: Recalculate • Above 2.326 Below Between Outside