Could you please reply / feedback on these 2 discussions?

Thank you

1.The binomial and normal distributions are two of the most prime probability distributions in statistic. The binomial concept can be developed into the normal distribution. The distribution was deliberated by the French mathematician Abraham de Moivre (1667-1754) and overdue the German mathematician Carl Friedrich Gauss (1777-1855), to which work was important about the normal distribution, the work of the mathematician give us a base on which a great deal of the theory of statistical inference is based. Vacuum manufacture build, a new Vacuum product name as "SS999" with mean being of 60 months and standard deviation of 6 months. Decide the minimal guarantee time period, which give permit to manufacture to payback on only 3.5% of the SS999 Vacuum?

As example: we have mean=60 and here deviation is=6, mass-production like to pay off only 3.5% of the vacuum. Therefore, we have discovered time period proportional to 3.5/100 =0.035. using Normal value (probability, mean, standard deviation), its show normal value (0.035,60,6) =49.13 months. Rounding it off nearest integer, we will get 49 months, thus minimum guarantee time period will be 49 months.

My second example for washing machine Normal value (0.95,36,5) it will give you 44.22 months which is a wrong answer because if I want to pay 5%, then the outcome should be less than the mean value of 36 moths in order to obtain normal distribution, we realize that 50% of data is more than mean and 50% data is underneath the mean, therefore value of 44 months will outcome in paid off. Now we have to look for the lesser 5%, nevertheless the top 5% reason the top 5% means we are going to make payment for lower the 95% washer machine, so only 5% pay off, have need of guarantee time period should be NORMINV (0.05,36,5) =27.76 or 28 months (rounded).

Reference

https://www.coursehero.com/tutors-problems/Statistics-and-Probability/19044913-Topic-Normal-distributions-can-be-used-for-many-purposesOne-purpos

2.Normal distribution represents data that is symmetrically distributed without any skews. On a graph, normally distributed data will make a bell curve with most of the data being towards the middle of the data set. Some key characteristics about normal distributions are that they have the exact same mean, median and mode, because of symmetrical distribution half of the data sits above the mean and half sits below, it is measured with the mean and standard deviations representing the peak and the stretched of the curve respectively. The empirical rule tells where most of the values in the data set are, 68% under the first standard deviation, 95% under the second, and 99.7 under the third. The following are examples of normal distributions and probabilities.

Ex] Suppose that there is a group of children whose growth is being measured, and the data is spread in a normal distribution. Consider that to grow an inch normally takes about 6 months with a standard deviation of 1.5 months. If we want to ensure that 75% of them will grow an inch, we could use:

=NORMINV(0.75,6,1.5)

to determine how long to wait before measuring, which would give 7.01 months. This means that we would need to wait 7 months in between measurement to ensure that 75% of them reach the growth requirements.

Ex] Consider a new phone is being released. The battery for the phone will remain healthy for approximately 60 months before the battery starts to lose its capacity with a standard deviation of 8 months. If we want to offer a discount to replace the battery for 40% of the phones (60% will have to pay in full to get a replacement) then we could use:

=NORMINV(0.4,60,8)

which would give 57.97 months. This means that we would set the last day for discounted battery replacement to be 57.97 months after their purchase.

References:

Bhandari, P. (2021, January 19). Normal distribution: Examples, formulas, & uses. Retrieved May 06, 2021, fromhttps://www.scribbr.com/statistics/normal-distribution/(Links to an external site.)

Normal distributions review (article). (n.d.). Retrieved May 06, 2021, from https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/normal-distributions-library/a/normal-distributions-review