During September, the average temp of laurel lake is 64.2 degrees. the standard deviation is 3.2 degrees. Assume the variable is normally distributed. For the randomly selected day, find the probability that the temp will be
a. above 62 degrees
b. below 67 degrees
c. between 65 degrees and 68 degree
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities for the various Z scores.
A camera store sells 40 pairs of binoculars per week on average with a standard deviation of 6. What is the probability that the store will sell more than 52 pairs binoculars in any week?
To find the probability for each scenario, we will use the normal distribution with the given average temperature and standard deviation.
a. To find the probability that the temperature is above 62 degrees, we need to find the area under the normal distribution curve to the right of 62 degrees.
b. To find the probability that the temperature is below 67 degrees, we need to find the area under the normal distribution curve to the left of 67 degrees.
c. To find the probability that the temperature is between 65 degrees and 68 degrees, we need to find the area under the normal distribution curve between these two values.
The steps to calculate these probabilities are as follows:
1. Standardize the values:
To work with the standard normal distribution, we need to standardize the given values using the formula:
Z = (X - μ) / σ
where Z is the standard score, X is the given value, μ is the mean, and σ is the standard deviation.
2. Find the corresponding cumulative probability:
Using a standard normal distribution table or a calculator, look up the cumulative probability for each standardized value found in step 1. This will give you the area under the normal distribution curve to the left of each value.
3. Calculate the desired probability:
To find the probability for each scenario, use the cumulative probabilities found in step 2 according to the following formulas:
a. The probability above 62 degrees is equal to 1 minus the cumulative probability to the left of 62 degrees.
P(X > 62) = 1 - P(X ≤ 62)
b. The probability below 67 degrees is equal to the cumulative probability to the left of 67 degrees.
P(X < 67) = P(X ≤ 67)
c. The probability between 65 degrees and 68 degrees is equal to the cumulative probability to the left of 68 degrees minus the cumulative probability to the left of 65 degrees.
P(65 < X < 68) = P(X ≤ 68) - P(X ≤ 65)
By following these steps, you can find the probabilities for each scenario.