As described in z-distribution the answers are given below:
a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows: (747, 853).
b) The sampling error at 95% confidence level is of: $35.78.
What is a z-distribution ?
The normal distribution with a mean of 0 and a standard deviation of 1 is referred to as the standard normal distribution (also known as the Z distribution) (the green curves in the plots to the right). It is frequently referred to as the bell curve since the probability density graph resembles a bell.
solution:
The bounds of the confidence interval are given as follows:
In which:
is the sample mean.
z is the critical value.
n is the sample size. is the standard deviation for the population.
The parameters for this problem are given as follows:
Hence the lower bound of the interval is of:
800 - 200 x 1.96/square root of 55 = 747.
The upper bound of the interval is of:
800 + 200 x 1.96/square root of 55 = 853.
The sampling error for a sample size of 120 is calculated as follows:
200 x 1.96/square root of 120 = $35.78.
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Answer:
c
Step-by-step explanation:
X/4 + 12 = 5
to isolate the variable the first step is to subtract 12 from both sides
x/4 + 12 - 12 = 5 - 12
x/4 = -7
next, to get rid of the division by 4, multiply both sides by 4
(x/4)*4 = -7*4
x = -28
The population after 20 weeks will be 403.42
in which is the initial population.
Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.
We are required to find the number of bacteria present after 10 weeks.
let the number of bacteria present at t is x.
So,
dx/dt∝x
dx/dt=kx
1/x dx=k dt
Now integrate both sides.
=
log x=kt+log c----------1
Put t=0
log =0 +log c ( shows the population in beginning)
Cancelling log from both sides.
c=
So put c= in 1
log x=kt+log
log x=log 
+log
log x=log 
x=
We have been given that the population triples in a week so we have to put the value of x=2 and t=1 to get the value of k.
2=
2=
log 2=k
We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.
x=
x=
x=
x=403.42
Hence the population after 20 weeks will be 403.42 in which is the initial population.
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The given question is incomplete as the question incudes the following:
Calculate the population after 20 weeks.
