The following is the distribution of the readings obtained with a Geiger counter of the number of parti-cles emitted by a radioactive substance in 100 successive 40-second intervals:Number ofparticles Frequency5–9 110–14 1015–19 3720–24 3625–29 1330–34 235–39 1(a) Verify that the mean and the standard deviation ofthis distribution are x = 20 and s = 5.(b) Find the probabilities that a random variable havinga normal distribution with μ = 20 and σ = 5 will take ona value less than 9.5, between 9.5 and 14.5, between 14.5and 19.5, between 19.5 and 24.5, between 24.5 and 29.5,between 29.5 and 34.5, and greater than 34.5.(c) Find the expected normal curve frequencies for thevarious classes by multiplying the probabilities obtainedin part (b) by the total frequency, and then test at the 0.05level of significance whether the data may be looked uponas a random sample from a normal population.
The following is the distribution of the readings
obtained with a Geiger counter of the number of parti-
cles emitted by a radioactive substance in 100 successive
40-second intervals:
Number of
particles Frequency
5–9 1
10–14 10
15–19 37
20–24 36
25–29 13
30–34 2
35–39 1(a) Verify that the mean and the standard deviation of
this distribution are x = 20 and s = 5.
(b) Find the probabilities that a random variable having
a
a value less than 9.5, between 9.5 and 14.5, between 14.5
and 19.5, between 19.5 and 24.5, between 24.5 and 29.5,
between 29.5 and 34.5, and greater than 34.5.
(c) Find the expected normal curve frequencies for the
various classes by multiplying the probabilities obtained
in part (b) by the total frequency, and then test at the 0.05
level of significance whether the data may be looked upon
as a random sample from a normal population.
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