Answer:
<em>The probability of successes </em> P( x < 4 ) = 0.36138
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given 'n'=9
<em>The probability of success 'p' = 0.45</em>
<em> q = 1-p = 1-0.45 = 0.55</em>
<em>Let 'X' be the random variable in Binomial distribution</em>
<em></em><em></em>
<em></em><em></em>
<em></em>
<u><em>Step(ii):-</em></u>
<em>The probability of x successes in the n independent trials of the experiment</em>
= By using factorial notation
<em></em><em></em>
P( x < 4 ) = (0.55)⁹ + 9(0.45) (0.55)⁸ + 36 (0.45)² (0.55)⁷ +84 (0.45)³ (0.55)⁶
P( x < 4 ) = 0.004605+0.03391 + 0.1109855+ 0.21188
P( x < 4 ) = 0.36138
<u><em>Final answer:-</em></u>
<em>The probability of successes </em> P( x < 4 ) = 0.36138
<em></em>