According to a​ survey, 61​% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly​ selected, and the number cleared by arrest or exceptional means is recorded.   ​(a) Find the probability that exactly 40 of the murders were cleared. ​(b) Find the probability that between 35 and 37 of the​ murders, inclusive, were cleared. ​(c) Would it be unusual if fewer than 19 of the murders were​ cleared? Why or why​ not?

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According to a​ survey,
61​%
of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly​ selected, and the number cleared by arrest or exceptional means is recorded.
 
​(a) Find the probability that exactly
40
of the murders were cleared.
​(b) Find the probability that between
35
and
37
of the​ murders, inclusive, were cleared.
​(c) Would it be unusual if fewer than
19
of the murders were​ cleared? Why or why​ not?
​(a) The probability that exactly
40
of the murders were cleared is
 
.
​(Round to four decimal places as​ needed.)
​(b) The probability that between
35
and
37
of the​ murders, inclusive, were cleared is
 
.
​(Round to four decimal places as​ needed.)
​(c) Would it be unusual if fewer than
19
of the murders were​ cleared? Why or why​ not?
 
 
A.
​No, it would not be unusual because
19
is less than
μ−2σ.
 
B.
​Yes, it would be unusual because
19
is between
μ−2σ
and
μ+2σ.
 
C.
​Yes, it would be unusual because
19
is less than
μ−2σ.
 
D.
​No, it would not be unusual because
19
is between
μ−2σ
and
μ+2σ.
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