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6.3 (Areas under the normal curve and inverse 2015).notebook January 19, 2015
Students will be able find areas under the standard normal curve to answer probability questions.
WarmupFind the area between the two zscores.
6.3 Areas Under Any Normal Curve
Find the probability P(2.20 < z < 1.40)
2 1 0 1 2
z= 1.40 .9192z= 2.20 .0139
.9053
90.53%
Topic #72 and #73 are due on Tuesday
What warranty period would require the company to repair or replace only 15% of the motor scooters?
15%
2 1 0 1 2
Nordik's motor scooters have an average life of 2.3 years with standard deviation of 0.4 years.
Students will be able find areas under the standard normal curve to answer probability questions.
3. Find .1500 in the middle of the z chart.
6.3 Inverse Normal Distribution
2. change 15% to a decimal.
1. Draw it
Answer: 1.04
4. Decide which number it is closest too. Read to the left and up for z score.
6.3 (Areas under the normal curve and inverse 2015).notebook January 19, 2015
Find z so that 5% of the standard normal curve lies to the right of z.
Students will be able to change a normal curve into a standard normal curve and find areas under the standard normal curve to answer probability questions.
6.3 Inverse Normal Distribution
Answer: Between 1.64 and 1.65
.9500 is between the two zscores
z= 1.645
shade what this will look like.
? What % is to the left ?
3. Find .9500 in the middle of the z chart.
2. change 95% to a decimal.
6.3 (Areas under the normal curve and inverse 2015).notebook January 19, 2015
Accrotime is a company that manufactures quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 5 months, and the distribution of lifetimes is normal. average life µ =standard deviation σ =
6.3 Areas Under Any Normal Curve
b) If Accrotime does not want to make refunds for more than 12% of the watches it makes, how long should the guarantee period be (to the nearest month)?
Answer: 22 months
6.3 (Areas under the normal curve and inverse 2015).notebook January 19, 2015
6.3 Areas Under Any Normal Curve
Find the z value such that 78% of the standard normal curve lies between z and z.
Answer: ?? 1.23 < z < 1.23
1. Shade 78% of the middle.
2. That leaves 10078% = 22% unshade. 3. 22/2 means 11% in each tail
4. Look up .1100 in middle of chart
and read to the left and up.
5. Use symmetry for the other zscore.
Find z < 0 so that 33% of the standard normal curve lies between z and 0.
33%
z = 0z
Students will be able to change a normal curve into a standard normal curve and find areas under the standard normal curve to answer probability questions.
6.3 Inverse Normal Distribution
Answer: Between .95 and .96
z= .95 .1711z= .96 .1685
Closer to .95
z= .95
If 50% of the graph is left of the 0, 5033 = 17% left of the blue section.
PullHint: Need to know how much to the left of the blue.