The closing price of Schnur Sporting Goods, Inc., common stock is uniformly distributed between $16 and 29 per share.Exercises
What is the probability that the stock price will be:
More than $23?
Less than or equal to $19?
Do you mean uniformly or normally?
"Uniformly" would indicate equal frequency for all monetary values.
Of the 14 values, there are six values "more than $23." Thus it is 6/14 = 3/7 = 43%
This should help you to determine your answer to the second question.
To find the probability that the stock price will be more than $23 or less than or equal to $19, we need to calculate the proportions of the distribution in those ranges.
First, let's find the total range of the stock price distribution. The stock price is uniformly distributed between $16 and $29 per share, so the range is 29 - 16 = $13.
Now, let's calculate the range of prices that are more than $23. Since the price must be "more than" $23, it would include all prices between $23 and $29. The range in this case is 29 - 23 = $6.
To find the probability of a price being more than $23, we need to divide the range of prices more than $23 (6) by the total range (13):
Probability(Price > $23) = Range of Prices > $23 / Total Range
= 6 / 13
≈ 0.4615 or 46.15%
Next, let's calculate the range of prices that are less than or equal to $19. Since the price must be "less than or equal to" $19, it would include all prices between $16 and $19. The range in this case is 19 - 16 = $3.
To find the probability of a price being less than or equal to $19, we need to divide the range of prices less than or equal to $19 (3) by the total range (13):
Probability(Price ≤ $19) = Range of Prices ≤ $19 / Total Range
= 3 / 13
≈ 0.2308 or 23.08%
Therefore, the probability that the stock price will be more than $23 is approximately 46.15%, and the probability that the stock price will be less than or equal to $19 is approximately 23.08%.