Stitch Fix was founded in the apartment of its chief executive, Katrina Lake, six years ago.

Stitch Fix is an increasingly rare kind of start-up pursuing a public listing, because it has shown it can turn a profit. The question for investors is whether a company whose business could be swamped by Amazon — in this case, selling clothes over the internet — is a safe bet.

Stitch Fix priced its initial public offering at $15 a share on Thursday, below expectations for $18 to $20 a share, as it embarks upon a new life as a publicly traded company. At that price, Stitch Fix raised about $120 million and was valued at about $1.5 billion.

Yet going public is perhaps the least of the challenges that now confront the mail-order clothing service. When the company, based in San Francisco, begins trading on Friday — on the Nasdaq stock market, under the ticker “SFIX” — its viability as a stand-alone business will be a concern.

Founded six years ago out of the apartment of its founder, Katrina Lake, Stitch Fix was not an obvious candidate for business success. Customers have little choice in which clothing they receive, and it does not promote particularly huge discounts for brand-name dresses and shirts.

The way Stitch Fix works, in a nutshell: New customers fill out extensive forms listing their style preferences, clothing needs and price points. Computer programs then predict which items those customers are likely to want, and an army of 3,400 stylists refine those selections. Customers then receive five items via mail, shipping back articles they do not want free of charge.

Should a customer keep everything in a box — a “fix,” in the company’s jargon — they receive a 25 percent discount.

“I founded Stitch Fix to take on a very human problem: How do I find clothes I love?” Ms. Lake wrote in a letter to potential investors that is included in the company’s I.P.O. prospectus. “Spending a day at the mall, or devoting hours of time to sifting through millions of products online is time consuming, overwhelming and neither effective nor enjoyable. I knew there had to be another way.”

It is a business…