For the 900 trading days from January 2003 through July 2006, the daily closing
ID: 3354240 • Letter: F
Question
For the 900 trading days from January 2003 through July 2006, the daily closing price of IBM stock (in $) is well modelled by a Normal model with mean $80.96 and standard deviation $4.19. Use the 68-95-99.7 Rule to approximate the following probabilities rather than using technology to find the values above precisely. Complete parts (a) through (d). a) According to this model, what is the probability that on a randomly selected day in this period the stock price closed below $89.34 The probability is 97.5 %. Type an integer or a decimal.) b) According to this model, what is the probability that on a randomly selected day in this period the stock price closed above $93.53? The probability is 0.15% (Type an integer or a decimal.) c) According to this model, what is the probability that on a randomly selected day in this period the stock price closed between $68.39 and $80.96? The probability is 1% (Type an integer or a decimal.)Explanation / Answer
a) here as 89.34 is 2 std deviation from mean hence 97.5%
b)93.53 is 3 std deviation from mean therefore probability =0.15%
c) as 80.96 is at z=0 and 68.39 is at z =-3
therefore probability =50-0.15 =49.85%