The average admission charge for a movie is $6. if the distribution of movie admission charges is approximately normal with a standard deviation of $1, what is the probability that a randomly selected admission charge is less than $3.5?
You have to find a z-score
6 -3.50 divided by 1
Now that you have the z-score, you have to use a normal table or a calculator to find the area under the curve which gives you ght probability.
You will look for the area to the left of your z-score.
To find the probability that a randomly selected admission charge is less than $3.5, we need to calculate the area under the normal distribution curve up to $3.5.
First, we need to standardize the value $3.5 using the standard deviation and the mean of the distribution.
Z = (X - μ) / σ
Where:
Z is the standardized value,
X is the given value ($3.5),
μ is the mean of the distribution ($6),
σ is the standard deviation ($1).
Plugging in the values:
Z = (3.5 - 6) / 1
Z = -2.5
Next, we can use the standard normal distribution table or a calculator to find the area to the left of the standardized value -2.5. This area represents the probability that a randomly selected admission charge is less than $3.5.
Looking up the value in the standard normal distribution table (z-table), we find that the area to the left of -2.5 is approximately 0.0062.
Therefore, the probability that a randomly selected admission charge is less than $3.5 is approximately 0.0062, or 0.62%.