Question

A company has developed an "easystart" 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 3 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

0.25
0.20
Probability
0,15 -
0.10
0.05
0.00

Describe the shape of the probability distribution.

A) The shape of the probability distribution is skewed
to the left with a single peak at T = 27 times.

B) The shape of the probability distribution is Normally
distributed with a single peak at T = 27 times.

C) The shape of the probability distribution is skewed
to the right with a single peak at T = 27 times.

D) The shape of the probability distribution is roughly
symmetric with a single peak at T = 27 times.

E) The shape of the probability distribution is uniform
with a single peak at 7 = 27 times.


10
15
20
25
30
T = Number of times the mower starts on
the first push of the button

Answer 1

The probability distribution of the number of times the mower starts on the first push of the button is skewed to the left with a single peak at T = 27 times. It is most likely that the mower will start on the first push 27 times out of 30.

Let's describe the probability distribution of the number of times the mower starts on the first push of the button, assuming that the company's claim is true is that the probability the mower will start on any push of the button is 0.9.

This problem can be modeled by a binomial distribution with 30 trials and a probability of success of 0.9. The binomial distribution is a probability distribution that describes the number of successes in a sequence of independent trials, where each trial has two possible outcomes (success or failure).

The probability distribution of the number of times the mower starts on the first push of the button is shown in the histogram. The shape of the distribution is skewed to the left with a single peak at T = 27 times. This means that it is most likely that the mower will start on the first push 27 times out of 30. The probability of this happening is 0.23.

The probability of the mower starting on the first push less than 27 times is greater than the probability of the mower starting on the first push more than 27 times. This is because the probability of success (0.9) is higher than the probability of failure (0.1).