The trial court may discharge a juror who "becomes ill, or upon other good cause shown to the court is found to be unable to perform his or her duty . . . ." ( 1089.) While extreme inattentiveness due to sleeping may constitute good cause to discharge a juror, "'courts have exhibited an understandable reluctance to overturn jury verdicts on the ground of inattentiveness during trial. . . . Perhaps recognizing the soporific effect of many trials when viewed from a layman's perspective, these cases uniformly decline to order a new trial in the absence of convincing proof that the jurors were actually asleep during material portions of the trial. .' ." (People v. Bradford (1997) 15 Cal.4th 1229, 1349 (Bradford ).) "A juror must not be discharged for sleeping unless there is convincing proof the juror actually slept during trial. ." (People v. Bowers (2001) 87 Cal.App.4th 722, 731.) "Once a trial court is put on notice that good cause to discharge a juror may exist, it is the court's duty 'to make whatever inquiry is reasonably necessary' to determine whether the juror should be discharged. ." (People v. Espinoza (1992) 3 Cal.4th 806, 821.) The decision whether to investigate the possibility of juror misconduct rests within the sound discretion of the trial court. (People v. Ray (1996) 13 Cal.4th 313, 343.) "The court does not abuse its discretion simply because it fails to investigate any and all new information obtained about a juror during trial." (Ibid.) Mere speculation that a juror might have been sleeping or inattentive is insufficient to provide notice of good cause to discharge, and does not obligate a trial court to conduct an inquiry. (Espinoza, at p. 821.) A defendant has a constitutional right to a unanimous verdict by a fair and impartial jury. (Cal. Const., art. I, 16; U.S. Const., 6th & 14th Amends.; see also People v. Wheeler (1978) 22 Cal.3d 258, 265.) Consistent with this constitutional right, a trial court may discharge a sworn-in juror under some circumstances. Penal Code Section 1089 provides in relevant part: "If at any time, whether before or after the final submission of the case to the jury, a juror dies or becomes ill, or upon other good cause shown to the court is found to be unable to perform his or her duty, . . . the court may order the juror to be discharged and draw the name of an alternate, who shall then take a place in the jury box, and be subject to the same rules and regulations as though the alternate juror had been selected as one of the original jurors." "Removing a juror is, of course, a serious matter, implicating the constitutional protections defendant invokes. While a trial court has broad discretion to remove a juror for cause, it should exercise that discretion with great care." (People v. Barnwell (2007) 41 Cal.4th 1038, 1052.) "When a court is informed of allegations which, if proven true, would constitute good cause for a juror's removal, a hearing is required. " (Id. at p. 1051.) "A trial court facilitates review when it expressly sets out its analysis of the evidence, why it reposed greater weight on some part of it and less on another, and the basis of its ultimate conclusion that a juror was failing to follow the oath." (Id. at p. 1053.) On review, we must ensure that the grounds for a juror's disqualification "appear on the record as a '"'"demonstrable reality.'"'" . . . This standard 'indicates that a stronger evidentiary showing than mere substantial evidence is required to support a trial court's decision to discharge a sitting juror.' " (People v. Barnwell, supra, 41 Cal.4th at p. 1052.) "Under the demonstrable reality standard, . . . the reviewing court must be confident that the trial court's conclusion is manifestly supported by evidence on which the court actually relied." (Id. at p. 1053.)