Since he moved in Asda's progress has been breathtaking in what is one of the toughest businesses in the land.
The once proud retail chain, born out of a dairy operation, seemed on the rocky road to oblivion.
The shares bumped along at a humble 23p and it had acquired a jokey, cloth-cap image making it the target for many a stand-up comedian.
Under the Norman touch the change in Asda's fortunes has been dramatic. Now the group is a superstore front-runner. But is the pace beginning to tell?
NatWest Securities was the first to raise doubts. In May it lowered its growth targets because of disappointing clothing sales, a reduced store opening programme and escalating overheads. Although analysts Tony MacNeary and Mike Dennis were then prepared to stick with their pounds 304m forecast for the year ended April they have had second thoughts and trimmed their estimate to pounds 297m.
Even so, such a result would represent a not inconsiderable 18 per cent gain, well in line with Asda's high-performance profile.
Still, it could be argued that Mr Norman and his team have completed the easy part of the revival.
They have refocused the group, reshaped its organisation and given it a remarkable air of confidence and reliability. It has also emerged as the leading price-cutter and probably the most customer-friendly in the industry. Now Asda's management has to raise its game.
Philip Dorgan at Societe Generale Strauss Turnbull outlines the challenge. He says: "Long-term success depends upon the establishment of genuine points of difference.
"Asda needs to become the best in the industry in areas other than price because, as its sales densities narrow the gap with Tesco and its cost ratios fall, there is a natural limit to the extent that its operating margin can rise, given that it maintains its price advantage. It therefore needs to seek ways to enhance its margin mix". He is looking for profits, due on Thursday, to "easily exceed" his pounds 300m forecast.
The Asda dilemma is not helped by the advent of loyalty cards. So far it has not been tempted into a full-scale launch although it is testing the concept in some stores. An Asda card could, however, undermine its policy of being the deepest of the superstore price-cutters.
The group can look forward to at least one windfall this year. It has 40 per cent of Allied Carpets, due to be floated in the next month or so. The share sale could produce pounds 80m, assuming Asda sells all its Allied shares.
Asda shares are near their highest under the Norman reign. The chain has a stock market valuation approaching pounds 3.5bn. NatWest regards the shares as no more than a hold but SocGen is still a buyer.
Tomorrow a very different and smaller group produces results. Halma, valued at nearly pounds 500m, is an engineer, largely involved in environmental controls and safety devices. It, too, has an outstanding reputation to maintain.
The company has an enviable record - profits advancing for 20 years and the dividend inevitably lifted by 20 per cent.
Halma has never adopted a very high profile and is little known outside the market. It could be described as the conglomerate nobody has heard about. Yet by dominating niche businesses, able to sell products equally well at home and overseas, as well as putting through some rewarding takeovers it has kept profits moving.
Although its shares are below their peak another strong performance is expected. NatWest is looking for pounds 34m against pounds 29.2m with a dividend of 2.565p a share - giving the traditional 20 per cent increase.
Last week was another unexciting one for the market and with the continuing array of sporting attractions and the lack of investor interest there is little hope this week will produce much action.
Footsie is still well below the 4,000 points level many have embraced as their year-end target. Quite clearly it will have to enjoy a strong second six months to offer the bulls any success.
The market, not for the first time and certainly not for the last, has failed to perform to the anticipated pattern. A strong first-half year was expected to be followed by a weak second six months.
The blue chip index has, however, had an indifferent first six months with Footsie only 45 points above the level it started the year, although the supporting FT-SE 250 index has conformed much more to expectations, up more than 400 points.
But the second-liners are running out of steam. They have had a surprisingly uncertain time since the 250 index peaked at 4,568.5 towards the end of April. The market has suffered in recent months from significant domestic selling which does, however, seem to be ending.
The jittery global bond markets, inflationary worries and the political climate have also taken their toll. So has the failure of the expected takeover bonanza to extend beyond utilities.
The bulls do, however, have their own positive agenda. They point to an encouraging profit outlook with next year's estimates being raised, the possibility of yet another interest rate cut and tentative signs of a gilts rally. And, of course, bid hopes spring eternal.
Even so, unless they can discover a few more encouraging indicators it is beginning to look as if the market will at best drift for the rest of the year and it may not be long before the bulls start reining in their forecasts.