Answer:
The probability that the stock will sell for $85 or less in a year's time is 0.10.
Step-by-step explanation:
Let X = stock's price during the next year.
The random variable X follows a normal distribution with mean, μ = $100 + $10 = $110 and standard deviation, σ = $20.
To compute the probability of a normally distributed random variable we first need to compute the z-score for the given value of the random variable.
The formula to compute the z-score is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Compute the probability that the stock will sell for $85 or less in a year's time as follows:
Apply continuity correction:
P (X ≤ 85) = P (X < 85 - 0.50)
= P (X < 84.50)
[tex]=P(\frac{X-mu}{\sigma}<\frac{84.5-110}{20})[/tex]
[tex]=P(Z<-1.28)\\=1-P(Z<1.28)\\=1-0.89973\\=0.10027\\\approx0.10[/tex]
*Use a z-table for the probability.
Thus, the probability that the stock will sell for $85 or less in a year's time is 0.10.
