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Chapter 6: Q. 92 (page 429)

Easy-start mower? A company has developed an "easy-start" mower that cranks the engine with the push of a button. The company claims that the probability the mower will start on any push of the button is 0.9. Assume for now that this claim is true. On the next 30 uses of the mower, let T=the number of times it starts on the first push of the button. Here is a histogram of the probability distribution of T :

a. What probability distribution does T have? Justify your answer.

b. Describe the shape of the probability distribution.

Short Answer

Expert verified

(a)All the binomial conditions are fullfilled here. Thus, it could be said that T follows the binomial distribution.

(b)the distribution is skewed to the left.

Step by step solution

01

Part (a) Step 1: Given  Information

the figure is:

02

Part (a) Step 2: Simplification

Following requiremens are fulfilled by the random variable T.

1. Probability of success, that is, probability of of mower starting (p)which is equal to 0.90is fixed.

2. Number of pushes are fixed.

3. Trials of starting mower are independent of each other.

4. There are two outcomes, that is mower starts and does not said

All the binomial conditions are fullfilled here. Thus, it could be said that T follows the binomial distribution

03

Part (b) Step 1: Given information

The graph is

04

Part (b) Step 2: Simplification

The probability distribution shows that the left tail of the graph is substantially longer than the right tail, indicating that the distribution is skewed to the left.

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