No settlement of an action of a minor for personal injuries will be authorized or approved without the appearance of the minor in court, medical evidence as to the extent of the minor's injuries, and such further information as the court will deem necessary; provided, however, that if the petition of the guardian for the compromise of a minor's action is accompanied by:
(1) written medical evidence as to the minor's medical condition and his or her prognosis,(2) a statement under oath by the guardian certifying,(a) the present physical or mental condition of the minor, and(b) approval of the proposed settlement and distribution thereof;(3) a statement by counsel of his professional opinion of the probabilities of proof of defendant's negligence by plaintiff and the minor's negligence, if any, by defendant; and,(4) in the event that the minor is sixteen (16) years of age or over, his or her written approval of the proposed settlement and distribution thereof; the judge to whom said petition has been presented may approve the petition without requiring the appearance of the minor, his guardian or his doctor, in the event that he concludes that the information contained in the petition is sufficient to satisfy him that the proposed settlement adequately compensates the minor and his guardian for the injuries sustained and expenses incurred.