Design specifications for filling a bottled soda claim that bottles should contain 350-360 milliliters of liquid. sample data indicate that the bottles contain an average of 355 milliliters of liquid, with a standard deviation of 2 milliliters. is the filling operation capable of meeting the design specifications?

It is high likely that the filling operation is capale of meeting design specifications.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Is the filling operation capable of meeting the design specifications?

It will be capable if it is highly likely that the specifications will be met. A probability is said to be high likely when it is of at least 95%.

In this case, the probability of containing between 350 and 360 ml of liquid is the pvalue of Z when X = 360 subtracted by the pvalue of Z when X = 350.

X = 360

has a pvalue of 0.9938.

X = 350

has a pvalue of 0.0062.

This means that there is a 0.9938 - 0.0062 = 0.9876 = 98.76% probability that the filling operation is capable of meeting the design specifications. It is high likely that the filling operation is capale of meeting design specifications.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.