The average life of a certain type of small motor is 10 years with a standard deviation

A guarantee of 6.24 years should be offered.

Step-by-step explanation:

Problems of normally distributed samples are 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:

If she is willing to replace only 3% of the motors that fail, how long a guarantee should be offered?

The 3rd percentile, that is, the value of X when Z has a pvalue of 0.03. So X when Z = -1.88.

A guarantee of 6.24 years should be offered.

Step-by-step explanation:

I think you mean missing angle.

This can be solved by using the triangle sum theorem. It states that the 3 angles of a triangle always add up to 180°. We just have to subtract the other 2 angles from 180°. 180 - (45 + 30) = 180 - 75 = 105.