376 Words2 Pages

Data File 3
Chapter Five
1) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?
The answer is 49.85%
99.7% = {µ- 3δ=1000 : µ+ 3δ=4000} 99.7/2 = 49.85%
2) The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?
68/95/99.7 rule: 1/2/3 µ=370 δ= 5 µ+ δ=375 Z= (375-370)/5= 5/5= 1 therefore the percentage under the rule is 68% 68/2 as deviation is to both sides
34% to either side
3) The amount of Jen’s monthly phone bill is normally distributed with a mean of $60 and a standard deviation of $12. Fill in the blanks:
68% of her phone bills are between $________72______ and $________48______.
µ=60 δ= 12 µ+δ = 72 µ-δ= 48
4) The amount of Jen’s monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.
43.28 = 50 - 13.44%
X= µ±zδ X=50 ± z(10) X= 50± 0.7(10) = 57 OR 43 75th and 25th
43 being lower is 25th
5) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?
X= 0.30 + z(0.01) 0.32= 0.30 + z(0.01) 0.02= z(0.01) z=2
68/95/99.7 rule: 1/2/3
95/2= 47.5%
6) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be

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