Throwing exceptions from constructors

I’m having a debate with a co-worker about throwing exceptions from constructors, and thought I would like some feedback.

Is it OK to throw exceptions from constructors, from a design point of view?

Lets say I’m wrapping a POSIX mutex in a class, it would look something like this:

class Mutex {
public:
  Mutex() {
    if (pthread_mutex_init(&mutex_, 0) != 0) {
      throw MutexInitException();
    }
  }

  ~Mutex() {
    pthread_mutex_destroy(&mutex_);
  }

  void lock() {
    if (pthread_mutex_lock(&mutex_) != 0) {
      throw MutexLockException();
    }
  }

  void unlock() {
    if (pthread_mutex_unlock(&mutex_) != 0) {
      throw MutexUnlockException();
    }
  }

private:
  pthread_mutex_t mutex_;
};

My question is, is this the standard way to do it? Because if the pthread mutex_init call fails the mutex object is unusable so throwing an exception ensures that the mutex won’t be created.

Should I rather create a member function init for the Mutex class and call pthread mutex_init within which would return a bool based on pthread mutex_init‘s return? This way I don’t have to use exceptions for such a low level object.