Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $75 and standard deviation $20. Round your answers to three decimal places, if necessary. a. What is the probability that a randomly selected customer spends less than $85 at this store? b. What is the probability that a randomly selected customer spends between $65 and $85 at this store? c. What is the probability that a randomly selected customer spends more than $45 at this store? d. Find the dollar amount such that 75% of all customers spend no more than this amount. e. Find the dollar amount such that 80% of all customers spend at least this amount. f. Find two dollar amounts, equidistant from the mean, such that 90% of all customer purchases are between these values. 5th percentile 95th percentile

a. 0.691

b. 0.382

c. 0.933

d. $88.490

e. $58.168

f. 5th percentile: $42.103

95th percentile: $107.897

Step-by-step explanation:

We have, for the purchase amounts by customers, a normal distribution with mean $75 and standard deviation of $20.

a. This can be calculated using the z-score:

The probability that a randomly selected customer spends less than $85 at this store is 0.691.

b. We have to calculate the z-scores for both values:

The probability that a randomly selected customer spends between $65 and $85 at this store is 0.382.

c. We recalculate the z-score for X=45.

The probability that a randomly selected customer spends more than $45 at this store is 0.933.

d. In this case, first we have to calculate the z-score that satisfies P(z<z*)=0.75, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

Then, we can calculate X as:

75% of the customers will not spend more than $88.49.

e. In this case, first we have to calculate the z-score that satisfies P(z>z*)=0.8, and then calculate the X* that corresponds to that z-score z*.

Looking in a standard normal distribution table, we have that:

Then, we can calculate X as:

80% of the customers will spend more than $58.17.

f. We have to calculate the two points that are equidistant from the mean such that 90% of all customer purchases are between these values.

In terms of the z-score, we can express this as:

The value for z* is ±1.64485.

We can now calculate the values for X as:

5th percentile: $42.103

95th percentile: $107.897

step-by-step explanation:

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral