One year consumers spent an average of $23 on a meal at a resturant. Assume that

Question

One year consumers spent an average of $23 on a meal at a resturant. Assume that the amount spent on a resturant meal is normally distributed and that the standard deviation is $4. Complete parts (a) through (c) below a. What is the probability that a randomly selected person spent more than $24? P(X > $24-LI (Round to four decimal places as needed.) b. What is the probability that a randomly selected person spent between $13 and $20? P($13 eX $20)-L(Round to four decimal places as needed.) C. Between what two values will the middle 95% of the amounts 01 cash spent fall The middle 95% or the amounts or cash spent will fall between X S and X= $ 4D Round to the nearest cent as needed.)

Explanation / Answer

SolutionA:

mean=23

sd=4

P(X>24)

P(Z>24-23/4)

P(Z>0.25)

using R

pnorm(-0.25)

0.4012937

ANSWER:0.4013

SolutionB:

P(13<X<20)

P(13-23/4<Z<20-23/4)

P(-2.5<Z-0.75)

=0.2204

ANSWER:0.2204

Solutionc:

lower limit=mean-2sigma=23-2*4=23-8=15

upper limit=mean+2 sigma=23+2*4=23+8=31

between 15 and 31

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