Question 1177608
**Step 1: Find the standard deviation**

We know that the visit times are normally distributed with a mean (µ) of 8.2 minutes. We also know that 79% of the visits last less than 10 minutes. This information allows us to find the standard deviation (σ) of the distribution.

* Let X be the random variable representing the time spent by a person visiting the dentist.
* We are given P(X < 10) = 0.79.
* We can standardize this value by finding the z-score corresponding to a cumulative probability of 0.79. Using a standard normal table or calculator, we find that the z-score is approximately 0.81.

Now, using the z-score formula:

```
z = (x - µ) / σ
```

We can plug in the values:

```
0.81 = (10 - 8.2) / σ
```

Solving for σ:

```
σ ≈ 2.22 minutes
```

**Step 2: Find the probability of a visit lasting less than 8.2 minutes**

Since the mean is 8.2 minutes, the probability of a visit lasting less than 8.2 minutes is simply 0.5 (because the normal distribution is symmetric around the mean).

**Step 3: Find the probability of fewer than 16 people out of 35 having visits less than 8.2 minutes**

Now we have a binomial distribution problem.

* n = 35 (number of trials)
* p = 0.5 (probability of success, i.e., a visit lasting less than 8.2 minutes)
* We want to find P(X < 16), where X is the number of people with visits less than 8.2 minutes.

We can use the binomial probability formula or a binomial calculator to find this probability. Using a calculator, we get:

```
P(X < 16) ≈ 0.214
```

**Therefore, the probability that fewer than 16 out of 35 randomly chosen people have visits lasting less than 8.2 minutes is approximately 0.214.**