The probability P(x<10), where x is the number of surveys returned, is 0.9806 or 98.06.
To find the probability P(x<10), where x is the number of surveys returned, we can use the binomial probability formula:

where:
n is the number of trials (number of surveys sent),
k is the number of successful trials (number of surveys returned),
p is the probability of success (probability a person returns the survey),
1−p is the probability of failure.
In this case:
n=30 (30 surveys sent),
p=0.27 (27% probability of returning the survey),
1−p=0.73 (probability of not returning the survey).
To find P(x<10), we need to sum the probabilities for x=0,1,2,…,9. This can be calculated using the binomial probability formula:

The binomial probability formula is given by:

Now, let's calculate each term:

Now, let's sum up these probabilities:

The result is approximately 0.9806 or 98.06.