Question

PART 1

31 people were surveyed and reported the amount of money they spend on a typical date night. The results were roughly bell-shaped with a mean of $35 and standard deviation of $20. Construct a confidence interval at a 98% confidence level.

Give your answers to two decimal places.

PART 2

A variable x is normally distributed with mean 19 and standard deviation 6.
Round your answers to the nearest hundredth as needed.

a) Determine the z-score for x=29.

1. z=

b) What value of x has a z-score of 1.83?

1. x=

PART 3
A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. Express answer as a fraction.
(a) The card drawn is a 10
The probability is :     

(b) The card drawn is a red card
The probability is :     

(c) The card drawn is a diamond.
The probability is :

Answer 1

part1:

98% confidence interval for is

- t * S / sqrt( n) < < + t * S / sqrt( n)

35 - 2.327 * 20/ sqrt(31) < < 35 + 2.327 * 20 / sqrt(31)

26.64 < < 43.36

98% CI is ( 26.64, 43.36)

Part2:

a)

b)

X = 6 * 1.83 + 19 = 29.98

Part3:

a) There are 4 , 10 cards  in the dec,Since there are 52 cards, the probability of getting a 10 card in the first draw is 4/52.

b) There are 26 red cards  in the dec,Since there are 52 cards, the probability of getting a red card in the first draw is 26/52.

c) There are 13 diamonds in the dec, Since there are 52 cards, the probability of getting a diamond in the first draw is 13/52.