Question

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual? Probability is 0.12, which is unusual as it is less than 5% Probability is 0.12, which is usual as it is not less than 5% Probability is 0.88, which is unusual as it is greater than 5% Probability is 0.88, which is usual as it is greater than 5% Flag this Question

Question 2 2 pts Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. Find the probability that a randomly selected bill will have an amount greater than $173, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual? Probability is 0.04, which is unusual as it is not less than 5% Probability is 0.04, which is usual as it is less than 5% Probability is 0.04, which is usual as it is not less than 5% Probability is 0.04, which is unusual as it is less than 5%

Answer 1

Question 1)

Given,

= 8.21 , = 1.90

We convert this to standard normal as

P(X < x) = P( Z < x - / )

So,

P(X < 6) = P( Z < 6 - 8.21 / 1.90)

= P( Z < -1.1632)

= 1 - P( Z < 1.1632)

= 1 - 0.8776

= 0.1224

Probability is greater than 0.05, so this event is usual.

Which is usual as it is greater than 5%, probability is 0.12.

Question 2)

Given, = 108.43 , = 36.98

We convert this to standard normal as

P(X < x) = P( Z < x - / )

So,

P(X > 173) = P( Z > 173 - 108.43 / 36.98 )

= P( Z > 1.7461)

= 1 - P( Z < 1.7461)

= 1 - 0.9596

= 0.0406

Probability is 0.04, which is unusual as it is less than 5%.