1) the variable Z has a standard normal distribution a) find the number z that h
ID: 3300323 • Letter: 1
Question
1) the variable Z has a standard normal distribution a) find the number z that has cumulative proportion 0.78 b) find the number Z such that the event Z>z has proportion 0.22 ( show work please)
2) we assumed that the NAEP U.S. history scores for twelfth-grade students are approximately Normal with the reported mean and standard deviation, N(288,32). Let's check that assumption. In addition to means and standard deviations, you can find selected percentiles for the NAEP assessments. for the twelfth-grade U.S. history scores, the following percentiles are reported. ( show work)
Percentile Score 10% 246 25% 276 50% 290 75% 311 90% 328Explanation / Answer
Question 1:
From the standard normal tables we get:
P(Z < 0.7722) = 0.78
Therefore the value of z here is 0.7722
b) From previous part as we have, P(Z < 0.7722) = 0.78,
Therefore, P(Z > 0.7722) = 1 - 0.78 = 0.22
Therefore the value of z here is also 0.7722
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