# Statistics

1. The area of activity room has a normal distribution with a mean of 100m^2 and a S.D of 15m^2.

What is the area of a room being in the top 10% of room area?

2. Bags of floor packed by a particular machine have masses which are normally distributed with mean 500g and S.D 20g,

2% of the bags are rejected for being underweight and 1% of the bags are rejected for being over weight,

Between what range of values should the mass of a bag of flour lie if it is to be accepted?

### 1 個解答

• 6 年前
最愛解答

1.

The area of activity room has a normal distribution with a mean of 100 m² and a s.d. of 15 m².

What is the area of a room being in the top 10% of room area?

Solution

From the normal table, the 90% quantile of a standard normal distribution is about 1.282.

[Note: the more accurate value from Excel is =NORM.S.INV(0.9) = 1.281551566]

The required area is 100 + 1.282(15) = 119.23 m².

2.

Bags of floor packed by a particular machine have masses which are normally distributed with mean 500 g and s.d. 20 g, 2% of the bags are rejected for being underweight and 1% of the bags are rejected for being over weight.

Between what range of values should the mass of a bag of flour lie if it is to be accepted?

Solution

From the normal table, the 99% quantile of a standard normal distribution is about 2.326.

[Note: the more accurate value from Excel is =NORM.S.INV(0.99) = 2.326347874]

From the normal table, the 2% quantile of a standard normal distribution is about -2.054.

[Note: the more accurate value from Excel is =NORM.S.INV(0.02) = -2.053748911]

The required range is from 500 + (-2.054)(20) g to 500 + (2.326)(20) g, i.e., from 458.92 g to 546.52 g.