Answer: 0.9591
Step-by-step explanation:
Given : The probability that a person likes ice cream is p=0.80.
Sample size : n= 1000
Using the normal approximation to the binomial ,
[tex]\mu=np=1000(0.80)=800\\\\\sigma=\sqrt{np(1-p)}\\\\=\sqrt{1000(0.80)(0.20)}\approx12.65[/tex]
Let x be the random variable that represents the number of people like ice cream.
Now, the probability that 822 or fewer people selected like ice cream will be :-
[tex]P(x\leq882)=P(z\leq\dfrac{822-800}{12.65})\\\\=P(z\leq1.74)[/tex]
[∵ [tex]z=\dfrac{x-\mu}{\sigma}[/tex]]
[tex]=0.9591[/tex] [using p-value table for z]
Hence, the required probability = 0.9591
