The closing price of Schnur Sporting Goods, Inc., common stock is uniformly distributed between $17 and 35 per share.
What is the probability that the stock price will be:
More than $31?
Less than or equal to $23?
To find the probability that the stock price will be more than $31, we need to determine the proportion of the distribution that falls above $31.
Given that the closing price is uniformly distributed between $17 and $35, we can calculate the range of the distribution as:
Range = $35 - $17 = $18
To find the proportion of the distribution above $31, we need to calculate the range from $31 to $35 and divide it by the total range:
Range above $31 = $35 - $31 = $4
Probability (Stock price > $31) = Range above $31 / Total Range
= $4 / $18
= 4/18
= 2/9
Hence, the probability that the stock price will be more than $31 is 2/9.
To find the probability that the stock price will be less than or equal to $23, we need to determine the proportion of the distribution that falls below or equal to $23.
Again, we can calculate the range of the distribution as:
Range = $35 - $17 = $18
To find the proportion of the distribution below or equal to $23, we need to calculate the range from $17 to $23 and divide it by the total range:
Range below or equal to $23 = $23 - $17 = $6
Probability (Stock price ≤ $23) = Range below or equal to $23 / Total Range
= $6 / $18
= 6/18
= 1/3
Hence, the probability that the stock price will be less than or equal to $23 is 1/3.
To find the probability of the stock price being more than $31, we need to calculate the area under the probability density function (PDF) curve for the range above $31.
First, let's determine the total range of the stock price. The stock price is uniformly distributed between $17 and $35, which means the total range is $35 - $17 = $18.
To find the probability for a specific range, we divide the desired range by the total range. So, for the stock price to be more than $31, the desired range is $35 - $31 = $4.
The probability of the stock price being more than $31 is therefore (desired range) / (total range) = $4 / $18 = 4/18 = 2/9, which is approximately 0.2222 or 22.22%.
Now, let's find the probability of the stock price being less than or equal to $23.
The desired range is $23 - $17 = $6.
Again, we divide the desired range by the total range: $6 / $18 = 6/18 = 1/3, which is approximately 0.3333 or 33.33%.
Therefore, the probability that the stock price will be more than $31 is approximately 22.22%, and the probability that the stock price will be less than or equal to $23 is approximately 33.33%.
uniform between 17 and 35 so over a range of 35-17 = 18
let height of rectangle be 1
then area between 17 and 35 is 18
area from 31 to 35 = 4
so 4/18 = .222 for >31
area from 17 to 23 = 6
6/18 = .333