Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $100 and standard deviation $10. What is the probability that a randomly selected customer spends less than $105 at this store?

69.15% probability that a randomly selected customer spends less than $105 at this store

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What is the probability that a randomly selected customer spends less than $105 at this store?

This is the pvalue of Z when X = 105. So

has a pvalue of 0.6915

69.15% probability that a randomly selected customer spends less than $105 at this store

The probability that a randomly selected customer spends less than $105 at this store is 0.6915 or 69.15%

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Mean of the purchase amounts by customers entering a popular retail store = $ 100

Standard deviation of the purchase amounts by customers entering a popular retail store = $ 10

2. What is the probability that a randomly selected customer spends less than $105 at this store?

For calculating the probability, we need to find the z-score first, this way:

X = 105

z-score = (X - μ)/σ

Replacing with the values we have:

z-score = 105 - 100/10

z-score = 5/10 = 0.5

Now, let's calculate the probability, using the z-table:

p (z = 0.5) = 0.6915

The probability that a randomly selected customer spends less than $105 at this store is 0.6915 or 69.15%

step-by-step explanation:

from the graph attached below:

domain of graph is the value of x for which the given function profit function p(x) is defined.

(a) the domain represents the number of years for which the outlet will earn a profit.

range of profit function defines the lowest to highest value of profit earned.

(b) the range of this function is (0 , 160 ). for this function, the range represents the outlet's profit earned.

i believe the answer is 68cm

step-by-step explanation:

i just took 34 x 2 because the space between v and y is the same as y to k.