The figure below shows a frequency and relative-frequency distribution for the heights of female students attending a college. Records show that the mean height of these students is 64.5 inches and that the standard deviation is 1.8 inches. Use the given information to complete parts (a) through (c). a. The area under the normal curve with parameters H = 64.5 and o = 1.8 that lies to the left of 63 is 0.2100. Use this information to estimate the percent of female students who are shorter than 63 inches. 21 % (Type an integer or a decimal. Do not round.) Frequency Height (in.) Relative freq. O f b. Use the relative-frequency distribution to the left to obtain the exact percentage of female students who are 60-under 61 0.0070 61-under 62 9 0.0314 shorter than 63 inches. 62-under 63 25 0.0871 % 63-under 64 62 0.2160 64-under 65 94 0.3275 (Type an integer or a decimal. Do not round.) 65-under 66 62 0.2160 66-under 67 25 0.0871 67-under 68 6. 0.0209 68-under 69 0.0070 287 1.0000
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![The figure below shows a frequency and
relative-frequency distribution for the heights of female
students attending a college. Records show that the
mean height of these students is 64.5 inches and that the
standard deviation is 1.8 inches. Use the given
information to complete parts (a) through (c).
a. The area under the normal curve with parameters
H = 64.5 and o = 1.8 that lies to the left of 63 is 0.2100.
Use this information to estimate the percent of female
students who are shorter than 63 inches.
21 %
(Type an integer or a decimal. Do not round.)
Frequency
Height (in.)
Relative freq. O
f
b. Use the relative-frequency distribution to the left to
obtain the exact percentage of female students who are
60-under 61
2
0.0070
61-under 62
0.0314
shorter than 63 inches.
62-under 63
25
0.0871
63-under 64
62
0.2160
64-under 65
94
0.3275
(Type an integer or a decimal. Do not round.)
65-under 66
62
0.2160
66-under 67
25
0.0871
67-under 68
6.
0.0209
68-under 69
2
0.0070
287
1.0000](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95f2bc5f-d8f9-4abe-ba61-1ee4e5d35b88%2F1fa6d527-8a6b-4865-88e3-51ce6254c988%2Fdsva9w_processed.jpeg&w=3840&q=75)
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(a)
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