Use the following scenario to answer the next 6 questions. let x be a

Use the following scenario to answer the next 6 questions. Let x be a binomial random variable with
n = 10 and p =.4. Find the following values:
1) P(x = 4)
2) P(x ≤ 4)
3) P(x > 4)
 
4) P(x ≥ 4)
5) E(x) =np=
6) Standard Deviation = √npq, where q = 1 – p
Use the following scenario to answer the next 5 questions. As a way of fund raising, you decide to set up a hot dog stand, after a few weeks of doing this you sell 8 hot dogs every 10 minutes.
7) What is the probability you will sell 3 or less hot dogs in 10 minutes?
8) If you need to sell more than 3 hot dogs in 10 minutes to breakeven, what is the probability that you will break even in the next 10 minutes?
9) What is the expected number of hot dogs sold in 1 minute?
10) What is the expected number in 3 minutes?
11) What is the probability of selling exactly 3 hot dogs in 3 minutes?
Use the following scenario to answer the next 3 questions. A volunteer ambulance service handles 0 to 5 service calls on any given day. The probability distribution for the number of service calls is as follows.
Number of service calls probability
0 .10
1 .15
2 .30
3 .20
4 .15
5 .10
12) What is the expected number of service calls?
13) What is the variance in the number of service calls?
14) What is the standard deviation?