In studying a random sample of 20 automotive batteries, the confidence interval (0.22,0.33) was constructed for the population standard deviation of the batteries' reserve capacity in hours. This population standard deviation should be less than 0.26 hour. Does the confidence interval suggest that the variation in the batteries' reserve capacities is at an acceptable level? Explain your reasoning.

NO.

Step-by-step explanation:

From the question, we are given a random sample of 20 automotive batteries, a confidence interval =(0.22,0.33). Also, the population standard deviation is said to be less than 0.26 hour.

The confidence interval does NOT suggest that the variation in the batteries' reserve capacities is at an acceptable level.

REASON: If you look at the confidence interval, we can see that it contains the value for the standard deviation that is 0.26 and even MORE value than 0.26.

This does not give us any suggestion that the standard deviation is less than 0.26.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

from the sentence, "tomorrow morning, akiko will arrive an hour late" depicts a third person perspective because it doesn't use any pronoun to replace akiko, the subject of the sentence, and it is in singular form since akiko is only one person.