![josiahsurfer](/avatars/1137.jpg)
josiahsurfer
15.08.2020 •
Mathematics
The time required to cook a pizza at a neighborhood pizza joint is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes. Find the time for each event.
Solved
Show answers
More tips
- F Food and Cooking How to Make Cottage Cheese at Home: Simple and Quick Recipe with Step By Step Instructions...
- O Other What is a Disk Emulsifier and How Does it Work?...
- F Family and Home What does a newborn need?...
- F Family and Home Choosing the Right Car Seat for Your Child: Tips and Recommendations...
- F Food and Cooking How to Get Reconfirmation of Registration?...
- C Computers and Internet How to Get Rid of Spam in ICQ?...
- A Art and Culture Who Said The Less We Love a Woman, the More She Likes Us ?...
- F Family and Home How to Get Rid of Your Neighbors?...
- S Society and Politics How Could Nobody Know About the Dead Mountaineers?...
- H Health and Medicine How to Cure Adenoids?...
Answers on questions: Mathematics
- M Mathematics And explain too! ! i am a prime number between 40 & 50. if you add one to me, the sum of all prime factors of that composite number is 15. what number am i?...
- M Mathematics The kelly family went to dinner at applebees. if their bill...
- M Mathematics What whole number comes right after 102...
- M Mathematics The graph shows a scatter pilot and a linear model of joanna s height, in inches, for various ages. what is the best interpretation of the y-intercept of the line?...
- M Mathematics Is the height of a rocket a function of time? justify. a) no; the atmosphere is constantly changing. b) no; at any given time wind resistance can vary. c) no; at any given time,...
- M Mathematics Compare and contrast how to graph: x = 5 and y = –3....
- M Mathematics Find the missing values on the diagram below. Assume that each line is evenly divided. my teacher gave me a c- because I didn t show my work but I found the answer online and don...
- M Mathematics When outliers are removed, how does the mean change?...
- M Mathematics What is the value of x? Answer must be a decimal...
- M Mathematics Pls answer this question i really need it :/...
Ответ:
(a) the time for the event of the highest 5% is 15.29 minutes.
(b) the time for the event of the lowest 50% is 12 minutes.
(c) the time for the event of the middle 95% is 8.08 minutes and 15.92 minutes.
(d) the time for the event of the lowest 80% is 13.68 minutes.
Step-by-step explanation:
We are given that the time required to cook a pizza at a neighborhood pizza joint is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes.
Let X = the time required to cook a pizza at a neighborhood pizza joint.
The z-score probability distribution for the normal distribution is given by;
Z =
~ N(0,1)
where,
= mean time = 12 minutes
(a) We have to find the time for the event of the highest 5%, that means;
P(X > x) = 0.05 {where x is the required time}
P(
>
) = 0.05
P(Z >
) = 0.05
Now, in the z table, the critical value of x that represents the top 5% of the area is given as 1.645, i.e;
x = 12 + 3.29 = 15.29 minutes.
Hence, the time for the event of the highest 5% is 15.29 minutes.
(b) We have to find the time for the event of the lowest 50%, that means;
P(X < x) = 0.50 {where x is the required time}
P(
<
) = 0.50
P(Z <
) = 0.50
Now, in the z table, the critical value of x that represents the lowest 50% of the area is given as 0, i.e;
x = 12 + 0 = 12 minutes.
Hence, the time for the event of the lowest 50% is 12 minutes.
(c) We have to find the time for the event of the middle 95%, that means we have to find the time for the event of 2.5% and above 97.5%;
Firstly, the time for the event of the lowest 2.5%, i.e;
P(X < x) = 0.025 {where x is the required time}
P(
<
) = 0.025
P(Z <
) = 0.025
Now, in the z table, the critical value of x that represents the lowest 2.5% of the area is given as -1.96, i.e;
x = 12 - 3.92 = 8.08 minutes.
Firstly, the time for the event of the below 97.5%, i.e;
P(X < x) = 0.975 {where x is the required time}
P(
<
) = 0.975
P(Z <
) = 0.975
Now, in the z table, the critical value of x that represents the top 2.5% of the area is given as 1.96, i.e;
x = 12 + 3.92 = 15.92 minutes.
Hence, the time for the event of the middle 95% is 8.08 minutes and 15.92 minutes.
(d) We have to find the time for the event of the lowest 80%, that means;
P(X < x) = 0.80 {where x is the required time}
P(
<
) = 0.80
P(Z <
) = 0.80
Now, in the z table, the critical value of x that represents the lowest 80% of the area is given as 0.8416, i.e;
x = 12 + 1.68 = 13.68 minutes.
Hence, the time for the event of the lowest 80% is 13.68 minutes.
Ответ:
I believe it is A
Step-by-step explanation:
Let me know if it is wrong