Question

hello, please write down each step on how you got the answers. thank you for your help.

1. Fifty-eight percent of adults plan to purchase a Fitbit next year. You randomly select 200 adults and ask them if they plan to buy a Fitbit next year. What is the probability that at least 120 of these adults will say “Yes”?

Answer 1

Here we have given that 58% of adults plan to purchase a Fitbit next year(P).

Convert this percentage into decimal from ,P=0.58

Here we selected n=200 adults

We have to find probability of at least 120 out of 200 says "yes"

p=120/200=0.60

At least 120 out of 200 says yes of purchase FItbit next year is same as

Convert p in to z-score by using below formula

z=1.43

Use excel to find this probability

=NORMSDIST(1.43)

But this syntax give you P(z<1.43)=0.9236

Here we need P(Z>1.43)

Hence P(Z>1.43)=1-P(Z<1.43)

=0.0764

The probability that at least 120 of these adults will say “Yes” is 0.0764.