A study was conducted that found $46.9 \%$ of all smartphone users in the US had an iPhone. Suppose you were to randomly sample 40 US smartphone users. What is the probability that at least 22 of them had an iPhone?

Use a binomial distribution to answer this question. Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.654321 then you would type 0.65

Step 1 ：A study found that 46.9% of all smartphone users in the US had an iPhone. If we randomly sample 40 US smartphone users, we want to find the probability that at least 22 of them have an iPhone.

Step 2 ：We can use a binomial distribution to solve this problem. The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial, often referred to as 'success' and 'failure'. In this case, 'success' is a smartphone user having an iPhone.

Step 3 ：We have 40 trials (the 40 smartphone users we are sampling), and the probability of success on each trial is 46.9%, or 0.469 when expressed as a decimal.

Step 4 ：We want to find the probability of at least 22 successes. This is the same as finding the sum of the probabilities of exactly 22, 23, 24, ..., 40 successes.

Step 5 ：We calculate the binomial probability for each number of successful trials from 22 to 40, and then sum these probabilities.

Step 6 ：The final probability is approximately 0.19, or 19% when expressed as a percentage.

Step 7 ：Final Answer: The probability that at least 22 out of 40 randomly sampled US smartphone users have an iPhone is \(\boxed{0.19}\).