matematikk.net

1 H&M, a retail clothing company, operates two types of clothing stores in shopping malls.
One type specializes in clothes for men (H&M Man), and the other in clothes for women (H&M Woman).
The sales from a men’s clothing store average kr. 8,000,000 annually, and those from a women’s clothing
store average kr. 6,750,000 annually. The standard deviation of sales among men’s stores is kr. 1,000,000
annually, and among women’s stores is kr. 1,250,000. In a typical shopping mall, the company operates
one men’s store and one women’s store.


A)The rent for the spaces in the shopping mall costs kr. 300 per square meter. Both types of stores
occupy 2,500 square meters. What is the expected value and standard deviation of total sales in
excess of the rent costs?

B) If labor and other expenses (such as the cost of clothing that is sold) to operate the two stores at the
mall costs the company kr 7,500,000 annually, do you think there is a good chance that the company
might lose money?

I need help with these two questions

Rentekostnader: $r = 300\cdot 2\cdot 2500 = 1500000$
Salgsinntekter: $s = 6750000 + 6250000 = 13000000$
$d =s - r: 13000000 - 1500000 = 11500000$

Forventet $d$ er her den samme som $d$

Standardavviket i mannsavdelingen:$ s_m = 1000000$
Standardavviket i kvinneavdelingen:$ s_k = 1250000$
Standardavvikket i de to av delingene til sammen: $s = \sqrt{s_m^2 + s_k^2} \approx 1600000$
Her har vi tatt oss den frihet å regne salget i herre -og kvinneavdelingene som uavhengige størrelser. Noe de nok ganske sikkert ikke er, men vi har ingen opplysninger om hvordan de samvarierer og setter dermed denne samvariasjonen til null. Vi går også ut fra at $d$ er normalfordelt.

Lønnsutgifter og andre kostnader: 7500000

$d - 2s = 11500000 -2\cdot 1600000 = 8300000$
Her ser vi at selv med to standardavvik fra forventet inntekt, vil inntekten $ d = 8300000$ være større enne de resterende utgiftene $7500000$
Sjansene er derfor små, mindre enn 5%, for at firmaet vil tape penger.