Outside a home, there is a 6-key keypad that can be used to open the garage if the correct four-digit code? is entered. (a) how many codes are possible? (b) what is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?

The total number of codes is found with

This formula is applied when we have to find combinations where the order matters, and each element can be used more than once, as happens with codes, there can be repetitions of numbers.

So, represents the total number of elements which are 6, and represents the total digits per code, which are 4.

Replacing these values, we have

This means there are 1296 possible codes.

Now, if the owner doesn't remember the code, the probability of entering the correct code on the first try would be

This means that it's nearly impossible to enter the right code at once.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;