Arthur, the ruler of Avalon, has asked for your help with the economy of his country. Arthur's economic minister provides you wi
1 answer:
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Answer:
- <u>1. 0.0808</u>
- <u>2. 0.5371</u>
- <u>3. 58.2%</u>
<u></u>
Explanation:
The first part of the question, with the input data, is missing.
This is missing part:
- <em>Assume that X, the starting salary offer for education majors, is normally distributed with a mean of $46,292 and a standard deviation of $4,320</em>
<em>Question 1: The probability that a randomly selected education major received a starting salary offer greater than $52,350 is ________</em>
Find the Z-score.
The Z-score is the standardized value of the random variable and represents the number of standard deviations the value of the random variable is away from the mean:
The<em> standard normal distribution</em> tables give the cumulative probabilities as the cumulative area under the bell-shaped curve. P(Z>1.40) is the area under the curve that is to the right of Z = 1.40 or, what is the same, P(Z<-1.40) is the area to the left of Z = - 1.40.
Using the former, the table indicates P(Z>1.40) = 0.0808, which is 8.08%
<em>Question 2: The probability that a randomly selected education major received a starting salary offer between $45,000 and $52,350 is _______.</em>
Now you must find the area under the curve between the two Z-scores.
Then, you must find the area between Z = -0.30 and Z = 1.40
That is P(Z<1.40) - P(Z < - 0.30) = P(Z > - 1.40) - P(Z < - 0.30)
= 1 - P(Z< -1.40) - P( Z < -0.30)
Now, you can work with the area under the curve to the left of Z = - 1.40 and to the left of Z = - 0.30.
From the corresponding table, that is: 1 - 0.0808 - 0.3821 = 0.5371
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<em>Question 3. What percentage of education majors received a starting offer between $38,500 and $45,000? </em>
<em></em>
For X = $38,500:
For X = $45,000
Z = -0.3 (calculated above)
Then, you must find the area under the curve to the right of Z = - 1.80 and to the left of Z = - 0.3
- P (Z > - 1.80) - P (Z < - 0.3)
- 1 - P (Z < - 1.80) - P (Z < - 0.3)
- 1 - 0.0359 - 0.3821 = 0.582 = 58.2%