A random sample of 100 visitors to a popular theme park spent an average of $142 on the trip with a standard deviation of $47.50. Which of the following would be the 98% confidence interval for the mean amount of money spent by all visitors to this theme park?
a. ($130.77, $153.23)
b. ($132.77, $151.43)
c. ($132.69, $151.31)
d. ($140.88, $143.12)

a) 98% confidence interval for the mean amount of money spent by all visitors to this theme park

($130.77, $153.23)

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 100

Given the average of $142 on the trip with a standard deviation of $47.50

mean of the sample (x⁻) =  $142

standard deviation σ = $47.50.

Confidence intervals:-

The 98% of confidence intervals

on calculation, we get

($130.95 , 153.04)

The confidence intervals are ($130.95 , 153.04)

Final -

Its nearly the given option its (a)

($130.77, $153.23)

the third picture

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true