Answer: 0.5438
Step-by-step explanation:
Given : Sample size : n=7
Probability of success : p=0.55
Using Normal approximation for binomial distribution , we have
[tex]\mu= np =7(0.55)=3.85[/tex]
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{7(0.55)(0.45)}=1.32[/tex]
The probability that the number x of correct answers is fewer than 4 is given by :-
[tex]P(x<4)=P(z<\dfrac{4-3.85}{1.32})\\\\=P(z<0.11)=0.5438[/tex]
Hence, the probability that the number x of correct answers is fewer than 4= 0.5438
