Solve The mean score of a competency test is 60, with a standard deviation of 5. Between what two values do about 68% of the values lie? (Assume the data set has a bell-shaped distribution.

Between 55 and 65

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 60

Standard deviation = 5

Between what two values do about 68% of the values lie?

By the Empirical Rule, within 1 one standard deviation of the mean. So from 60-5 = 55 to 60+5 = 75.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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