Answered

Discover a world of knowledge and get your questions answered at IDNLearn.com. Ask anything and receive thorough, reliable answers from our community of experienced professionals.

If the amount of time to prepare and deliver a pizza from MOD PIZZA is normally distributed with a mean of 20 minutes and standard deviation of 5 minutes.
Determine the percent of pizzas that were prepared and delivered:
(a) Between 20 and 25 minutes (b) In less than 18 minutes
( c ) If MOD PIZZA advertises that the Pizza is free if it takes more than 30 minutes to deliver, what percent of the pizza will be free?

I need to answer a,b and c - it is not mutiple choice. I also need to show all relevant steps and plus I really want to understand how to do this! I am completely stuck on this one and its due tonight. Please help!! :) Ill give badges, brainliest, thanks, all of that for whoever can help me!

Sagot :

Using the normal distribution, we have that:

a) 34.13% of pizzas were prepared and delivered between 20 and 25 minutes.

b) 34.46% of pizzas were prepared and delivered in less than 18 minutes.

c) 2.28% of the pizza will be free.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 20, \sigma = 5[/tex]

For item a, the probability is the p-value of Z when X = 25 subtracted by the p-value of Z when X = 20, hence:

X = 25:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{25 - 20}{5}[/tex]

Z = 1

Z = 1 has a p-value of 0.8413.

X = 20:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20 - 20}{5}[/tex]

Z = 0

Z = 0 has a p-value of 0.5.

0.8413 - 0.5 = 0.3413.

Hence 34.13% of pizzas were prepared and delivered between 20 and 25 minutes.

For item b, the probability is the p-value of Z when X = 18, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{18 - 20}{5}[/tex]

Z = -0.4

Z = -0.4 has a p-value of 0.3446.

34.46% of pizzas were prepared and delivered in less than 18 minutes.

For item c, the proportion is one subtracted by the p-value of Z when X = 30, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 20}{5}[/tex]

Z = 2

Z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228, hence 2.28% of the pizza will be free.

More can be learned about the normal distribution at https://brainly.com/question/28135235

#SPJ1

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.