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gavmur [86]
3 years ago
5

A local car wash is inviting customers to join the concierge club

Mathematics
1 answer:
Ghella [55]3 years ago
7 0

Answer:

i guess this question miss the options to follow.

In any case the answer  

You can see that 6 washes is 30 dollars so that would make each wash $5 and all other answers can be proven wrong or not proven to be true.

good luck

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A prticular type of tennis racket comes in a midsize versionand an oversize version. sixty percent of all customers at acertain
svetlana [45]

Answer:

a) P(x≥6)=0.633

b) P(4≤x≤8)=0.8989 (one standard deviation from the mean).

c) P(x≤7)=0.8328

Step-by-step explanation:

a) We can model this a binomial experiment. The probability of success p is the proportion of customers that prefer the oversize version (p=0.60).

The number of trials is n=10, as they select 10 randomly customers.

We have to calculate the probability that at least 6 out of 10 prefer the oversize version.

This can be calculated using the binomial expression:

P(x\geq6)=\sum_{k=6}^{10}P(k)=P(6)+P(7)+P(8)+P(9)+P(10)\\\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\geq6)=0.2508+0.215+0.1209+0.0403+0.006=0.633

b) We first have to calculate the standard deviation from the mean of the binomial distribution. This is expressed as:

\sigma=\sqrt{np(1-p)}=\sqrt{10*0.6*0.4}=\sqrt{2.4}=1.55

The mean of this distribution is:

\mu=np=10*0.6=6

As this is a discrete distribution, we have to use integer values for the random variable. We will approximate both values for the bound of the interval.

LL=\mu-\sigma=6-1.55=4.45\approx4\\\\UL=\mu+\sigma=6+1.55=7.55\approx8

The probability of having between 4 and 8 customers choosing the oversize version is:

P(4\leq x\leq 8)=\sum_{k=4}^8P(k)=P(4)+P(5)+P(6)+P(7)+P(8)\\\\\\P(x=4) = \binom{10}{4} p^{4}q^{6}=210*0.1296*0.0041=0.1115\\\\P(x=5) = \binom{10}{5} p^{5}q^{5}=252*0.0778*0.0102=0.2007\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\\\P(4\leq x\leq 8)=0.1115+0.2007+0.2508+0.215+0.1209=0.8989

c. The probability that all of the next ten customers who want this racket can get the version they want from current stock means that at most 7 customers pick the oversize version.

Then, we have to calculate P(x≤7). We will, for simplicity, calculate this probability substracting P(x>7) from 1.

P(x\leq7)=1-\sum_{k=8}^{10}P(k)=1-(P(8)+P(9)+P(10))\\\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\leq 7)=1-(0.1209+0.0403+0.006)=1-0.1672=0.8328

7 0
3 years ago
A triangle has a base length of 12 inches and a height of 14 inches. From that
Paladinen [302]
A= bh(1/2)
a=12(14)(1/2)
a= 168(1/2)
a= 84inches
3 0
3 years ago
GEOMETRY Find the perimeter of the regular polygon.<br> 3(x - 1)<br> 5x - 6
viktelen [127]

Answer:

7.5

Step-by-step explanation:

6 0
3 years ago
Help plz I really need help could you show your work if you do it plz.
Vika [28.1K]
What do you need help with?
7 0
3 years ago
Meredith invested $5,500 into an account that earned 5% interest per year. When she cashed out the investment to use it as a dow
Andrej [43]

Answer:  B. 7739.05=5500(1.05)^t

Step-by-step explanation:

The formula to find the compound amount (compounded yearly):-

A=P(1+r)^t, where P is the principal amount invested,  is the rate of interest and t is time period.

As per given , we have

P=$5500    ,  r=5% = 0.05   and A =  $7,739.05.

Substitute all the values in the formula , we get

7739.05=5500(1+0.05)^t

7739.05=5500(1.05)^t

Hence, the equation describes Meredith's investment based on t, the number of years she kept the account open : 7739.05=5500(1.05)^t

5 0
3 years ago
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