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qaws [65]
3 years ago
9

A supervisor has determined that the average salary of the employees in his department is $40,000 with a standard deviation of $

15,000. A sample of 25 of the employees’ salaries was selected at random. Assuming that the distribution of the salaries is normal, what is the probability that the average for this sample is between $36,000 and $42,000?
Mathematics
1 answer:
mihalych1998 [28]3 years ago
4 0

The z-score for 36,000 is (36,000 - 40,000) / (15,000 / √25) = -1.333

The z-score for 42,000 is (42,000 - 40,000) / (15,000 / √25) = 0.6667

P(36,000 < x < 42,000) = P(-1.3333 < z < 0.6667)

P(z < 0.6667) - P(z < -1.3333)

0.7475 - 0.0913

0.6562

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3 years ago
A skate ramp is 4.2 meters long. It rises up 1.7 meters. What’s is the angle of elevation to the nearest tenth of a degree?
Kipish [7]
Θ
=
arcsin
(
.7
4.2
)
≈
10
∘
Explanation:
We view the ramp as a right triangle. The hypotenuse is 4.2 and the vertical side .7, which is opposite the angle
θ
we seek.
sin
θ
=
.7
4.2
=
1
6
I'm going to finish the problem but I'll note if we were actually building the ramp we don't need to know the angle; this sine is sufficient.
θ
=
arcsin
(
1
6
)
θ
≈
10
∘
which I think is a pretty steep ramp for a wheelchair.
There will be another inverse sine that is the supplementary angle, around
170
∘
, but we can rule that out as a value for a ramp wedge angle.
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