Answer:
The probability that there will be at most 41 correct answers is 0.8790
Step-by-step explanation:
We can aproximate the probability by using a binomial distribution where:
p: A question on a test is answered correctly
n: number of responses
So, the mean of the distribution is given by:
[tex]\mu= n\times p= 140 \times 0.25=35[/tex]
and the standar deviation is given by:
[tex]\sigma=\sqrt{n\times p\times q} =\sqrt{n\times p\times (1-p)} =\sqrt{140\times 0.25\times 0.75} =5.123[/tex]
The normalized variable for 41 correct answers is:
[tex]z=\frac{x-\mu}{\sigma}=\frac{41-35}{5.123} =1.17[/tex]
Hence, the probability that there will be at most 41 correct answers is:
[tex]P(x<41)=P(z<1.17)=0.8790[/tex]
