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ile Edit View History Bookmarks Window Help 33%D Sat 4:43 PM ning.com O Save & End Certify Lesson:6.4 Finding Values of a Normally D. ASHLEY GOLSAN Question 8 of 10, Step 1 of 1 7/18 Correct The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.11 millimeters a diameters that separate the top 9 % and the bottom 9 % . as limits used to to the nearest hundredth, if necessary. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer Tables Keypad Answer if you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. Note: Selecting a cell will return the value associated with the column and row headers for that cei millimeters and millimeters Normal Table 0 to Normal Table-to - Normal Table-0 to 2 Submit Answer © 2018 Hawkes Learning

Explanation / Answer

A) For top 9%

P(X > x) = 0.09

Or, P((X - mean)/SD > (x - 5.11)/0.07) = 0.09

Or, P(Z > (x - 5.11)/0.07) = 0.09

Or, P(Z < (x - 5.11)/0.07) = 0.91

Or, (x - 5.11)/0.07 = 1.34

Or, x = 1.34 * 0.07 + 5.11

Or, x = 5.2

For bottom 9%

P(X < x) = 0.09

Or, P((X - mean)/SD < (x - 5.11)/0.07) = 0.09

Or, P(Z < (x - 5.11)/0.07) = 0.09

Or, (x - 5.11)/0.07 = -1.34

Or, x = -1.34 * 0.07 + 5.11

Or, x = 5

B) P(X > 81.2) = P((X - mean)/(SD/Sqrt (n)) > (81.2 - 83)/(9/sqrt(146))

= P(Z > -2.42)

= 1 - P(Z < -2.42)

= 1 - 0.0078 = 0.9922

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