Question

The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years ​(104 ​weeks) are shown to the right.

Answer 1

The expected number of mortgages approved per week and the standard deviation of the distribution are 2.019 and 0.024 respectively.

The expected number of mortgages approved per week :

• Mean = (Σfx ÷ Σf)

Expected Number approved = 210 ÷ 104 = 2.019

Hence, it is expected that 2.019 mortageahes would be approved per week.

The standard deviation :

• Variance = [Σ(Xi - x)² ÷ Σf]

• Standard deviation = √Variance

Variance = (59.5414 ÷ 104) = 0.0005698

Standard deviation = √0.0005698

Standard deviation = 0.024

Therefore, the expected value and standard deviation are 2.019 and 0.024 respectively.

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