Question 4 (15 points) (5 points) Suppose a deli sells morning newspaper deviati

Question

Question 4 (15 points) (5 points) Suppose a deli sells morning newspaper deviation of 20. Calculate using the normal distribution density function. a. s at an average of 15 per hour with a standard 1. 2. what is the probability that the deli will sell 10 newspapers in a given hour What is the probability that the deli will sell between 22 newspapers in a given hour? (5 points) Suppose you take a sample of 200 Lehman students. The average height is 65 inches (5'4") with a standard deviation of 5 inches. Using the Standard Normal Distribution: b. what would be the height in inches when the probability is 4.95% (0.0495) and when the probability is 95.05% (0.9505)? what would be the height if the probability is 99.01% (0.9901)? 1, 2, (5 points) The manager of a local Gap store estimates that on average the probability of a customer entering the store and will purchase something is 20% (0.20), Assume a Binomial distribution 1. What is the probability that 3 of the next 4 customers will make a purchase? 2. What is the probability that none of the next 4 customers will make a purchase? c.

Explanation / Answer

Solution:

a)

1.We are given,

Mean = m = 15   and Standard deviation = s = 20

We have to find P( X = 10 ) = ……?

Using excel, =NORMDIST(10,15,20,FALSE)

P( X = 10 ) = 0.01933

2.We have to find P( X = 22 ) = …………?

Using excel, =NORMDIST(22,15,20,TRUE)

P( X = 22 ) = 0.6368

b).

Here we are given, n = sample size = 200 , Mean = m = 65 and standard deviation = s = 5

1.We have to find value of x if P( Z < z ) = 0.0495

Formula : X = m+Z*s

First we have to find z using excel formula, =NORMSINV(0.0495)

Z = -1.650

Hence X = 56.75

Now We have to find value of x if P( Z < z ) = 0.9505

Formula : X = m+Z*s

First we have to find z using excel formula, =NORMSINV(0.9505)

Z = 1.650

Hence X = 73.25

2. We have to find value of x if P( Z < z ) = 0.9901

Formula : X = m+Z*s

First we have to find z using excel formula, =NORMSINV(0.9901)

Z = 2.330

Hence X = 76.65

Done

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